Question

The vector $z=3-4i$ is turned anticlockwise through an angle of 180${}^o$ and stretched $2.5$ 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. none of these

Answer 1

The correct option is B $\frac{-15}{2}+10i$

Given, $3-4i$ i.e.,$(3,4)$ lie in fourth quadrant in complex plane.
After turned anticlockwise through $180$ ${}^o$ 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 $-\frac{15}{2}+10i$