1. Tardigrade
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  4. Let the affix of 2-4 i be P. Then O P is rotated about O through an angle of 180° and is stretched 5 / 2 times. The complex number corresponding to the new position of P is

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Q. Let the affix of $2-4 i$ be $P$. Then $O P$ 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

Complex Numbers and Quadratic Equations

Solution:

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