Question

Let the affix of $2-4i$ be $P$. Then $OP$ is rotated about $O$ though an angle ${180}^0$ and is stretched $\frac{5}{2}$ times. Then show that complex number corresponding to the new position of $P$ is $-5+10i$.

Answer 1

If a complex number $z$ is rotated through an angle ${180}^0$, then it's new position is $-z$.

So, $2-4i$ is $-2+4i$ and stretching it $\frac{5}{2}$ times of previous complex number

i.e. $\frac{5}{2}(-2+4i)=-5+10i$