Question

Let the affix of $2-4i$ be $P$. Then $OP$ is rotated about $O$ through an angle of $180^{\circ }$ and is stretched $5/2$ times. The complex number corresponding to the new position of $P$ is

• A. $5-10i$
• B. $5+10i$
• C. $-5+10i$
• D. None of these

Answer 1

Answer: (C)

If a complex number $z$ is rotated through an angle $180^{\circ }$, then it's new position is $-z$.
So, $2-4i$ is $-2+4i$ and stretching it $5/2$ times means modulus $5/2$ times of previous complex number
i.e., $\frac{5}{2}(-2+4i)=-5+10i$