JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank

done Integral power of iota, Algebraic operations and Equality of complex numbers Total Questions - 67

• question_answer1)
  \[\sqrt{-2}\,\sqrt{-3}=\] [Roorkee 1978]
  A)
  \[\sqrt{6}\] done clear
  B)
  \[-\sqrt{6}\] done clear
  C)
  \[i\sqrt{6}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer2)
  If \[n\] is a positive integer, then which of the following relations is false
  A)
  \[{{i}^{4n}}=1\] done clear
  B)
  \[{{i}^{4n-1}}=i\] done clear
  C)
  \[{{i}^{4n+1}}=i\] done clear
  D)
  \[{{i}^{-4n}}=1\] done clear
  View Solution play_arrow

• question_answer3)
  If  \[n\] is a positive integer,  then \[{{\left( \frac{1+i}{1-i} \right)}^{4n+1}}\]=
  A)
  1 done clear
  B)
  - 1 done clear
  C)
  \[i\] done clear
  D)
  \[-i\] done clear
  View Solution play_arrow

• question_answer4)
  If \[{{\left( \frac{1+i}{1-i} \right)}^{m}}=1,\]then the least integral value of \[m\] is [IIT 1982; MNR 1984; UPSEAT 2001; MP PET 2002]
  A)
  2 done clear
  B)
  4 done clear
  C)
  8 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer5)
  If  \[{{(1-i)}^{n}}={{2}^{n}},\]then \[n=\] [RPET 1990]
  A)
  1 done clear
  B)
  0 done clear
  C)
  \[-1\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer6)
  The value of \[{{(1+i)}^{5}}\times {{(1-i)}^{5}}\] is [Karnataka CET 1992]
  A)
  - 8 done clear
  B)
  \[8i\] done clear
  C)
  8 done clear
  D)
  32 done clear
  View Solution play_arrow

• question_answer7)
  \[{{\left( \frac{1+i}{1-i} \right)}^{2}}+{{\left( \frac{1-i}{1+i} \right)}^{2}}\]is equal to
  A)
  \[2i\] done clear
  B)
  \[-2i\] done clear
  C)
  \[-2\] done clear
  D)
  \[2\] done clear
  View Solution play_arrow

• question_answer8)
  The value of  \[\frac{{{i}^{592}}+{{i}^{590}}+{{i}^{588}}+{{i}^{586}}+{{i}^{584}}}{{{i}^{582}}+{{i}^{580}}+{{i}^{578}}+{{i}^{576}}+{{i}^{574}}}-1=\]
  A)
  \[-1\] done clear
  B)
  - 2 done clear
  C)
  \[-3\] done clear
  D)
  - 4 done clear
  View Solution play_arrow

• question_answer9)
  \[1+{{i}^{2}}+{{i}^{4}}+{{i}^{6}}+.....+{{i}^{2n}}\]is [EAMCET 1980]
  A)
  Positive done clear
  B)
  Negative done clear
  C)
  Zero done clear
  D)
  Cannot be determined done clear
  View Solution play_arrow

• question_answer10)
  \[{{i}^{2}}+{{i}^{4}}+{{i}^{6}}+......\]upto \[(2n+1)\] terms = [EAMCET 1980; Kerala (Engg.) 2005]
  A)
  \[i\] done clear
  B)
  \[-i\] done clear
  C)
  1 done clear
  D)
  \[-1\] done clear
  View Solution play_arrow

• question_answer11)
  If \[i=\sqrt{-1}\], then \[1+{{i}^{2}}+{{i}^{3}}-{{i}^{6}}+{{i}^{8}}\] is equal to [RPET 1995]
  A)
  \[2-i\] done clear
  B)
  1 done clear
  C)
  3 done clear
  D)
  \[-1\] done clear
  View Solution play_arrow

• question_answer12)
  If \[{{i}^{2}}=-1\],  then the value of  \[\sum\limits_{n=1}^{200}{{{i}^{n}}}\]is [MP PET 1996]
  A)
  \[50\] done clear
  B)
  - 50 done clear
  C)
  0 done clear
  D)
  100 done clear
  View Solution play_arrow

• question_answer13)
  The value of the sum \[\sum\limits_{n=1}^{13}{({{i}^{n}}+{{i}^{n+1}})}\], where \[i=\sqrt{-1}\], equals [IIT 1998]
  A)
  \[i\] done clear
  B)
  \[i-1\] done clear
  C)
  \[-i\] done clear
  D)
  0 done clear
  View Solution play_arrow

• question_answer14)
  The least positive integer \[n\] which will reduce \[{{\left( \frac{i-1}{i+1} \right)}^{n}}\] to a real number, is [Roorkee 1998]
  A)
  2 done clear
  B)
  3 done clear
  C)
  4 done clear
  D)
  5 done clear
  View Solution play_arrow

• question_answer15)
  The value of \[{{i}^{1+3+5+...+(2n+1)}}\] is [AMU 1999]
  A)
  i if n is even, - i if n is odd done clear
  B)
  1 if n is even, - 1 if n is odd done clear
  C)
  1 if n is odd, - 1 if n is even done clear
  D)
  i if n is even, - 1 if n is odd done clear
  View Solution play_arrow

• question_answer16)
  If \[\]\[x+\frac{1}{x}=2\cos \theta ,\] then x is equal to [RPET 2001]
  A)
  \[\cos \theta +i\,\sin \theta \] done clear
  B)
  \[\cos \theta -i\,\sin \theta \] done clear
  C)
  \[\cos \theta \pm i\,\sin \theta \] done clear
  D)
  \[\sin \theta \pm i\,\cos \theta \] done clear
  View Solution play_arrow

• question_answer17)
  The value of \[{{i}^{n}}+{{i}^{n+1}}+{{i}^{n+2}}+{{i}^{n+3}}\,,\,(n\in N)\] is [RPET 2001]
  A)
  0 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer18)
  The value of \[{{(1+i)}^{8}}+{{(1-i)}^{8}}\] is  [RPET 2001; KCET  2001]
  A)
  16 done clear
  B)
  - 16 done clear
  C)
  32 done clear
  D)
  - 32 done clear
  View Solution play_arrow

• question_answer19)
  \[{{(1+i)}^{10}}\], where \[{{i}^{2}}=-1,\] is equal to [AMU 2001]
  A)
  32 i done clear
  B)
  64 + i done clear
  C)
  24 i - 32 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer20)
  The value of \[{{(1+i)}^{6}}+{{(1-i)}^{6}}\] is  [RPET 2002]
  A)
  0 done clear
  B)
  27 done clear
  C)
  26 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer21)
  If \[{{i}^{2}}=-1\], then sum \[i+{{i}^{2}}+{{i}^{3}}+...\]to 1000 terms is equal to [Kerala (Engg.) 2002]
  A)
  1 done clear
  B)
  - 1 done clear
  C)
  i done clear
  D)
  0 done clear
  View Solution play_arrow

• question_answer22)
  If \[x=3+i\],  then \[{{x}^{3}}-3{{x}^{2}}-8x+15=\] [UPSEAT 2003]
  A)
  6 done clear
  B)
  10 done clear
  C)
  - 18 done clear
  D)
  - 15 done clear
  View Solution play_arrow

• question_answer23)
  The smallest positive integer \[n\]for which \[{{(1+i)}^{2n}}={{(1-i)}^{2n}}\]is  [Karnataka CET 2004]
  A)
  1 done clear
  B)
  2 done clear
  C)
  3 done clear
  D)
  4 done clear
  View Solution play_arrow

• question_answer24)
  The values of \[x\] and \[y\] satisfying the equation \[\frac{(1+i)x-2i}{3+i}\] \[+\frac{(2-3i)\,y+i}{3-i}=i\] are [IIT 1980; MNR 1987]
  A)
  \[x=-1,\,y=3\] done clear
  B)
  \[x=3,\,y=-1\] done clear
  C)
  \[x=0,\,y=1\] done clear
  D)
  \[x=1,y=0\] done clear
  View Solution play_arrow

• question_answer25)
  If \[{{z}_{1}}\] and \[{{z}_{2}}\] be two complex number, then  Re\[({{z}_{1}}{{z}_{2}})=\]
  A)
  Re \[({{z}_{1}}).\operatorname{Re}({{z}_{2}})\] done clear
  B)
  Re \[({{z}_{1}})\]. Im \[({{z}_{2}})\] done clear
  C)
  Im \[({{z}_{1}}).\operatorname{Re}\,({{z}_{2}})\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer26)
  \[\left( \frac{1}{1-2i}+\frac{3}{1+i} \right)\,\,\left( \frac{3+4i}{2-4i} \right)=\] [Roorkee 1979; RPET 1999; Pb. CET 2003]
  A)
  \[\frac{1}{2}+\frac{9}{2}i\] done clear
  B)
  \[\frac{1}{2}-\frac{9}{2}i\] done clear
  C)
  \[\frac{1}{4}-\frac{9}{4}i\] done clear
  D)
  \[\frac{1}{4}+\frac{9}{4}i\] done clear
  View Solution play_arrow

• question_answer27)
  Additive inverse of \[1-i\]is
  A)
  \[0+0i\] done clear
  B)
  \[-1-i\] done clear
  C)
  \[-1+i\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer28)
  \[\operatorname{Re}\frac{{{(1+i)}^{2}}}{3-i}\] =
  A)
  \[-1/5\] done clear
  B)
  1/5 done clear
  C)
  1/10 done clear
  D)
  -1/10 done clear
  View Solution play_arrow

• question_answer29)
  If \[(1-i)x+(1+i)y=1-3i,\] then  \[(x,y)=\]
  A)
  \[(2,-1)\] done clear
  B)
  \[(-2,\,1)\] done clear
  C)
  \[(-2,-1)\] done clear
  D)
  (2, 1) done clear
  View Solution play_arrow

• question_answer30)
  \[\frac{3+2i\sin \theta }{1-2i\sin \theta }\]will be real, if \[\theta \] =    [IIT 1976; EAMCET 2002]
  A)
  \[2n\pi \] done clear
  B)
  \[n\pi +\frac{\pi }{2}\] done clear
  C)
  \[n\pi \] done clear
  D)
  None of these [Where \[n\] is an integer] done clear
  View Solution play_arrow

• question_answer31)
  \[\frac{\sqrt{5+12i}+\sqrt{5-12i}}{\sqrt{5+12i}-\sqrt{5-12i}}=\]
  A)
  \[-\frac{3}{2}i\] done clear
  B)
  \[\frac{3}{2}i\] done clear
  C)
  \[-\frac{3}{2}\] done clear
  D)
  \[\frac{3}{2}\] done clear
  View Solution play_arrow

• question_answer32)
  If z and\[{z}'\] are complex numbers such that \[z.z'=z\], then \[z'=\]
  A)
  \[0+i\,0\] done clear
  B)
  \[1+0i\] done clear
  C)
  \[0+i\] done clear
  D)
  \[1+i\] done clear
  View Solution play_arrow

• question_answer33)
  If \[{{a}^{2}}+{{b}^{2}}=1,\] then \[\frac{1+b+ia}{1+b-ia}=\]
  A)
  1 done clear
  B)
  2 done clear
  C)
  \[b+ia\] done clear
  D)
  \[a+ib\] done clear
  View Solution play_arrow

• question_answer34)
  \[\frac{3+2i\sin \theta }{1-2i\sin \theta }\] will be purely imaginary, if \[\theta =\] [IIT 1976; Pb. CET 2003]
  A)
  \[2n\pi \pm \frac{\pi }{3}\] done clear
  B)
    \[n\pi +\frac{\pi }{3}\] done clear
  C)
  \[n\pi \pm \frac{\pi }{3}\] done clear
  D)
  None of these [Where \[n\] is an integer] done clear
  View Solution play_arrow

• question_answer35)
  The real part of  \[{{(1-\cos \theta +2i\sin \theta )}^{-1}}\]is [IIT 1978, 86]
  A)
  \[\frac{1}{3+5\cos \theta }\] done clear
  B)
  \[\frac{1}{5-3\cos \theta }\] done clear
  C)
  \[\frac{1}{3-5\cos \theta }\] done clear
  D)
  \[\frac{1}{5+3\cos \theta }\] done clear
  View Solution play_arrow

• question_answer36)
  If \[{{(x+iy)}^{1/3}}=a+ib,\]then \[\frac{x}{a}+\frac{y}{b}\]is equal to [IT 1982; Karnataka CET 2000]
  A)
  \[4({{a}^{2}}+{{b}^{2}})\] done clear
  B)
  \[4({{a}^{2}}-{{b}^{2}})\] done clear
  C)
  \[4({{b}^{2}}-{{a}^{2}})\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer37)
  \[{{\left\{ \frac{2i}{1+i} \right\}}^{2}}=\] [BIT Ranchi 1992]
  A)
  1 done clear
  B)
  \[2i\] done clear
  C)
  \[\alpha -i\beta \,(\alpha ,\beta \,\text{real),}\] done clear
  D)
  \[\left( \frac{3-4ix}{3+4ix} \right)=\] done clear
  View Solution play_arrow

• question_answer38)
  The real values of \[x\]and\[y\]for which the equation is \[(x+iy)\] \[(2-3i)\]= \[4+i\] is satisfied, are [Roorkee 1978]
  A)
  \[x=\frac{5}{13},y=\frac{8}{13}\] done clear
  B)
  \[x=\frac{8}{13},y=\frac{5}{13}\] done clear
  C)
  \[x=\frac{5}{13},y=\frac{14}{13}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer39)
  The real values of  \[x\] and \[y\] for which the equation \[({{x}^{4}}+2xi)-(3{{x}^{2}}+yi)=\]\[(3-5i)+(1+2yi)\] is satisfied, are [Roorkee 1984]
  A)
  \[x=2,y=3\] done clear
  B)
  \[x=-2,y=\frac{1}{3}\] done clear
  C)
  Both (a) and (b) done clear
  D)
   None of these done clear
  View Solution play_arrow

• question_answer40)
  The imaginary part of  \[\frac{{{(1+i)}^{2}}}{(2-i)}\]is
  A)
  \[\frac{1}{5}\] done clear
  B)
  \[\frac{3}{5}\] done clear
  C)
  \[\frac{4}{5}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer41)
  If \[z\ne 0\] is  a complex number, then
  A)
  \[\operatorname{Re}(z)=0\Rightarrow \operatorname{Im}({{z}^{2}})=0\] done clear
  B)
    \[\operatorname{Re}({{z}^{2}})=0\Rightarrow \operatorname{Im}({{z}^{2}})=0\] done clear
  C)
  \[\operatorname{Re}(z)=0\Rightarrow \operatorname{Re}({{z}^{2}})=0\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer42)
  If  \[\frac{5(-8+6i)}{{{(1+i)}^{2}}}=a+ib\], then\[(a,\,b)\] equals [RPET 1986]
  A)
  (15, 20) done clear
  B)
  (20, 15) done clear
  C)
  \[(-15,\,20)\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer43)
  The true statement is [Roorkee 1989]
  A)
  \[1-i<1+i\] done clear
  B)
  \[2i+1>-2i+1\] done clear
  C)
  \[2i>1\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer44)
  \[\frac{1-2i}{2+i}+\frac{4-i}{3+2i}=\] [RPET 1987]
  A)
  \[\frac{24}{13}+\frac{10}{13}i\] done clear
  B)
  \[\frac{24}{13}-\frac{10}{13}i\] done clear
  C)
  \[\frac{10}{13}+\frac{24}{13}i\] done clear
  D)
  \[\frac{10}{13}-\frac{24}{13}i\] done clear
  View Solution play_arrow

• question_answer45)
  \[a+ib>c+id\]can be explained only when
  A)
  \[b=0,c=0\] done clear
  B)
  \[b=0,d=0\] done clear
  C)
  \[a=0,c=0\] done clear
  D)
  \[a=0,d=0\] done clear
  View Solution play_arrow

• question_answer46)
  If \[x+iy=\frac{3}{2+\cos \theta +i\sin \theta },\]then \[{{x}^{2}}+{{y}^{2}}\] is equal to
  A)
  \[3x-4\] done clear
  B)
  \[4x-3\] done clear
  C)
  \[4x+3\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer47)
  If  \[\frac{{{(p+i)}^{2}}}{2p-i}=\mu +i\lambda ,\]then \[{{\mu }^{2}}+{{\lambda }^{2}}\] is equal to
  A)
  \[\frac{{{({{p}^{2}}+1)}^{2}}}{4{{p}^{2}}-1}\] done clear
  B)
  \[\frac{{{({{p}^{2}}-1)}^{2}}}{4{{p}^{2}}-1}\] done clear
  C)
  \[\frac{{{({{p}^{2}}-1)}^{2}}}{4{{p}^{2}}+1}\] done clear
  D)
  \[\frac{{{({{p}^{2}}+1)}^{2}}}{4{{p}^{2}}+1}\] done clear
  View Solution play_arrow

• question_answer48)
  If \[z=3-4i\], then  \[{{z}^{4}}-3{{z}^{3}}+3{{z}^{2}}+99z-95\]is equal to
  A)
  5 done clear
  B)
  6 done clear
  C)
  - 5 done clear
  D)
  - 4 done clear
  View Solution play_arrow

• question_answer49)
  If \[{{z}_{1}}=1-i\] and \[{{z}_{2}}=-2+4i\],  then  \[\operatorname{Im}\left( \frac{{{z}_{1}}{{z}_{2}}}{{{z}_{1}}} \right)=\]
  A)
  1 done clear
  B)
  2 done clear
  C)
  3 done clear
  D)
  4 done clear
  View Solution play_arrow

• question_answer50)
   If \[\frac{3x+2iy}{5i-2}=\frac{15}{8x+3iy}\], then
  A)
  \[x=1,y=-3\] done clear
  B)
  \[x=-1,y=3\] done clear
  C)
  \[x=1,y=3\] done clear
  D)
  \[x=-1,y=-3\]or \[x=1,\]\[y=3\] done clear
  View Solution play_arrow

• question_answer51)
  If \[\sum\limits_{k=0}^{100}{{{i}^{k}}}=x+iy\], then the values of \[x\] and \[y\]are
  A)
  \[x=-1,y=0\] done clear
  B)
   \[x=1,y=1\] done clear
  C)
  \[x=1,y=0\] done clear
  D)
  \[x=0,y=1\] done clear
  View Solution play_arrow

• question_answer52)
  If  \[z(1+a)=b+ic\] and \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=1\], then \[\frac{1+iz}{1-iz}=\]
  A)
  \[\frac{a+ib}{1+c}\] done clear
  B)
  \[\frac{b-ic}{1+a}\] done clear
  C)
  \[\frac{a+ic}{1+b}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer53)
   Let \[{{z}_{1}},{{z}_{2}}\] be two complex numbers such that \[{{z}_{1}}+{{z}_{2}}\] and \[{{z}_{1}}{{z}_{2}}\] both are real, then [RPET 1996]
  A)
  \[{{z}_{1}}=-{{z}_{2}}\] done clear
  B)
  \[{{z}_{1}}={{\bar{z}}_{2}}\] done clear
  C)
  \[{{z}_{1}}=-{{\bar{z}}_{2}}\] done clear
  D)
  \[{{z}_{1}}={{z}_{2}}\] done clear
  View Solution play_arrow

• question_answer54)
  If \[(x+iy)(p+iq)=({{x}^{2}}+{{y}^{2}})i\], then
  A)
  \[p=x,q=y\] done clear
  B)
  \[p={{x}^{2}},\,\,q={{y}^{2}}\] done clear
  C)
  \[x=q,y=p\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer55)
  \[A+iB\] form of \[\frac{(\cos x+i\sin x)(\cos y+i\sin y)}{(\cot u+i)(1+i\tan v)}\] is [Roorkee 1980]
  A)
  \[\sin u\cos v\,[\cos (x+y-u-v)+i\sin (x+y-u-v)]\] done clear
  B)
  \[\sin u\cos v\,[\cos (x+y+u+v)+i\sin (x+y+u+v)]\] done clear
  C)
  \[\sin u\cos v\,[\cos (x+y+u+v)-i\sin (x+y+u+v)]\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer56)
  If \[x,y\in R\]and \[(x+iy)(3+2i)=1+i\],  then \[(x,\,y)\] is
  A)
    \[\left( 1,\frac{1}{5} \right)\] done clear
  B)
  \[\left( \frac{1}{13},\frac{1}{13} \right)\] done clear
  C)
    \[\left( \frac{5}{13},\frac{1}{13} \right)\] done clear
  D)
    \[\left( \frac{1}{5},\frac{1}{5} \right)\] done clear
  View Solution play_arrow

• question_answer57)
  If  \[{{\left( \frac{1-i}{1+i} \right)}^{100}}=a+ib\],  then [MP PET 1998]
  A)
  \[a=2,b=-1\] done clear
  B)
  \[a=1,b=0\] done clear
  C)
  \[a=0,b=1\] done clear
  D)
  \[a=-1,b=2\] done clear
  View Solution play_arrow

• question_answer58)
  If  \[{{z}_{1}}=(4,5)\] and \[{{z}_{2}}=(-3,2)\]then  \[\frac{{{z}_{1}}}{{{z}_{2}}}\] equals [RPET 1996]
  A)
  \[\left( \frac{-23}{12},\frac{-2}{13} \right)\] done clear
  B)
    \[\left( \frac{2}{13},\frac{-23}{13} \right)\] done clear
  C)
    \[\left( \frac{-2}{13},\frac{-23}{13} \right)\] done clear
  D)
  \[\left( \frac{-2}{13},\frac{23}{13} \right)\] done clear
  View Solution play_arrow

• question_answer59)
  If \[z=1+i,\] then the multiplicative inverse of z2 is (where i = \[\sqrt{-1}\]) [Karnataka CET 1999]
  A)
  2 si done clear
  B)
  1 - i done clear
  C)
  - i/2 done clear
  D)
  i/2 done clear
  View Solution play_arrow

• question_answer60)
  If \[\,\left| \begin{align}   & \,6i\,\,\,\,\,-3i\,\,\,\,\,\,\,\,\,1 \\  & \,\,4\,\,\,\,\,\,\,\,\,3i\,\,\,\,\,\,-1 \\  & \,20\,\,\,\,\,\,\,\,3\,\,\,\,\,\,\,\,\,\,i \\ \end{align} \right|\,\]=\[x+iy\], then (x, y) is [MP PET 2000]
  A)
  (3, 1) done clear
  B)
  (1, 3) done clear
  C)
  (0, 3) done clear
  D)
  (0, 0) done clear
  View Solution play_arrow

• question_answer61)
  If \[a=\cos \,\theta +i\,\sin \,\theta ,\] then \[\frac{1+a}{1-a}=\] [Karnataka CET 2000]
  A)
  \[\cot \theta \] done clear
  B)
  \[\cot \frac{\theta }{2}\] done clear
  C)
  \[i\,\cot \frac{\theta }{2}\] done clear
  D)
  \[i\,\tan \frac{\theta }{2}\] done clear
  View Solution play_arrow

• question_answer62)
  Solving \[3-2yi={{9}^{x}}-7i\], where \[{{i}^{2}}=-1,\] for x and y real, we get [AMU 2000]
  A)
  \[x=0.5\,\,,\,\,y=3.5\] done clear
  B)
  \[x=5\,\,,\,\,y=3\] done clear
  C)
  \[x=\frac{1}{2}\,\,,\,\,y=7\] done clear
  D)
  \[x=0,\,y=\frac{3+7i}{2i}\] done clear
  View Solution play_arrow

• question_answer63)
  The complex number \[\frac{1+2i}{1-i}\] lies in which quadrant of the complex plane [MP PET 2001]
  A)
  First done clear
  B)
  Second done clear
  C)
  Third done clear
  D)
  Fourth done clear
  View Solution play_arrow

• question_answer64)
  The real part of \[\frac{1}{1-\cos \theta +i\,\sin \theta }\] is equal to [Karnataka CET 2001, 05]
  A)
  1/4 done clear
  B)
  1/2 done clear
  C)
  tan q/2 done clear
  D)
  1/1- cos q done clear
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• question_answer65)
  The statement \[(a+ib)<(c+id)\] is true for [RPET 2002]
  A)
  \[{{a}^{2}}+{{b}^{2}}=0\] done clear
  B)
  \[{{b}^{2}}+{{c}^{2}}=0\] done clear
  C)
  \[{{a}^{2}}+{{c}^{2}}=0\] done clear
  D)
  \[{{b}^{2}}+{{d}^{2}}=0\] done clear
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• question_answer66)
  The multiplication inverse of a number is the number itself, then its initial value is   [RPET 2003]
  A)
  i done clear
  B)
  - 1 done clear
  C)
  2 done clear
  D)
  - i done clear
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• question_answer67)
  If \[z=x+iy,\,{{z}^{1/3}}=a-ib\] and \[\frac{x}{a}-\frac{y}{b}=k\,({{a}^{2}}-{{b}^{2}})\]  then value of k equals [DCE 2005]
  A)
  2 done clear
  B)
  4 done clear
  C)
  6 done clear
  D)
  1 done clear
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