JEE Math Practice Question

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

1. A.$$\left(2 \sec \frac{11 \pi}{8}, \frac{11 \pi}{8}\right)$$
2. B.$$\left(2 \sec \frac{3 \pi}{8}, \frac{3 \pi}{8}\right)$$
3. C.$$\left(2 \sec \frac{5 \pi}{8}, \frac{3 \pi}{8}\right)$$
4. D.$$\left(2 \sec \frac{3 \pi}{8}, \frac{5 \pi}{8}\right)$$