Let $\mathrm{r}$ and $\theta$ respectively be the modulus and amplitude of the complex number $z=2-i\left(2 \tan \frac{5 \pi}{8}\right)$, then $(\mathrm{r}, \theta)$ is equal to

Question

$\left(2 \sec \frac{11 \pi}{8}, \frac{11 \pi}{8}\right)$

$\left(2 \sec \frac{3 \pi}{8}, \frac{3 \pi}{8}\right)$

$\left(2 \sec \frac{5 \pi}{8}, \frac{3 \pi}{8}\right)$

$\left(2 \sec \frac{3 \pi}{8}, \frac{5 \pi}{8}\right)$

Solution

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