A) \[{{x}^{2}}+{{y}^{2}}\]
B) \[\sqrt{{{x}^{2}}-{{y}^{2}}}\]
C) \[x+iy\]
D) \[x-iy\]
Correct Answer: D
Solution :
Given that \[\sqrt{a+ib}=x+iy\] \[\Rightarrow \] \[a+ib={{x}^{2}}-{{y}^{2}}+2i\,\,xy\] \[\Rightarrow \] \[a={{x}^{2}}-{{y}^{2}},\,\,b=2xy\] ? (i) Now, we assume \[\sqrt{a-ib}=x-iy\] \[\Rightarrow \] \[a-ib={{x}^{2}}-{{y}^{2}}-2i\,xy\] \[\Rightarrow \] \[a={{x}^{2}}-{{y}^{2}},\,\,b=2xy\] ? (ii) \[\therefore \] Eqs. (i) and (ii) are equal. \[\therefore \] Option is correct.
You need to login to perform this action.
You will be redirected in
3 sec
