(A) : The mod amplitude form of $\frac{1+7\mathrm{i}}{{(2-\mathrm{i})}^2}$ is $\sqrt{2}\mathrm{cis} \frac{3\mathrm{\pi }}{4}$

(R):The mod–amplitude form $\mathrm{z}=\mathrm{a}+\mathrm{ib} \mathrm{is} \mathrm{r} \mathrm{cis} \mathrm{\theta }$ where $\mathrm{r}=\left|\mathrm{z}\right|, \mathrm{\theta }$

is amplitude of z

$$\begin{gathered} \frac{1+7\mathrm{i}}{{(2-\mathrm{i})}^2}=\frac{1+7\mathrm{i}}{3-4\mathrm{i}}=\frac{(1+7\mathrm{i}) (3+4\mathrm{i})}{9+16} \\ =\frac{-25+25\mathrm{i}}{25} \\ =-1+\mathrm{i} \\ =\sqrt{2}\left(\frac{-1}{\sqrt{2}}+\frac{\mathrm{i}}{\sqrt{2}}\right) \\ =\sqrt{2} \mathrm{cis}\frac{3\mathrm{\pi }}{4} \\ \mathrm{R} : \mathrm{z}=\mathrm{a}+\mathrm{ib}=\mathrm{r} \mathrm{cis\theta }, \mathrm{r}=\left|\mathrm{z}\right|, \mathrm{\theta }=\mathrm{Amp}\left(\mathrm{z}\right) \end{gathered}$$

Both A,R are true, R is explanation for A.