Statement-1: If \[|{{z}_{1}}|=30,\,\,|{{z}_{2}}-(12+5i)|=6\], then maximum value of\[|{{z}_{1}}-{{z}_{2}}|\]is\[49\]. |
Statement-2: If \[{{z}_{1}},\,\,\,{{z}_{2}}\] are two complex numbers, then\[|{{z}_{1}}-{{z}_{2}}|\le |{{z}_{1}}|+|{{z}_{2}}|\]and equality holds when origin, \[{{z}_{1}}\] and \[{{z}_{2}}\] are collinear and \[{{z}_{1}},\,\,{{z}_{2}}\] are on the opposite side of the origin. |
A) Statement-1 is false, Statement-2 is true.
B) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
C) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
D) Statement-1 is true, Statement-2 is false.
Correct Answer: C
Solution :
\[{{C}_{1}}{{C}_{2}}=13\] \[{{r}_{1}}=30,\,\,{{r}_{2}}=6\] \[{{C}_{1}}{{C}_{2}}<{{r}_{1}}-{{r}_{2}}\]You need to login to perform this action.
You will be redirected in
3 sec