Question

The vector $z=3-4i$ is turned anticlockwise through an angle of ${180}^{\circ }$ and stretched $\frac{5}{2}$ times. The complex number corresponding to the newly obtained vector is ....

• A. $-\frac{15}{2}-10i$
• B. $-\frac{15}{2}+10i$
• C. $\frac{15}{2}+10i$
• D. $\frac{15}{2}-10i$

Answer 1

Answer: (B)

$-\frac{15}{2}+10i$

$z=3-4i$ lie in fourth quadrant in complex plane, after turned anticlockwise through ${180}^0$ this will lie in II quadrant, therefore, the number will be $-3+4i$ now after stretching it $2.5$ times i.e., multiplying by $2.5$, the required complex number will be

$\Rightarrow 2.5\times (-3+4i)$

$\Rightarrow -\frac{15}{2}+10i$

Hence, this is the answer.