Question

Find the multiplicative inverse of $7+24i$.

Answer 1

Fact: Multiplicative inverse of $z$ is given by $\frac{\overline{z}}{|z{|}^2}$

Here $z=7+24i$

So $|z|=\sqrt{7^2+{24}^2}=25$

And $\overline{z}=7-24i$

So inverse is $\frac{7-24i}{625}$