MathematicsMedium53×since 2002Q3218Let r\mathrm{r}r and θ\thetaθ respectively be the modulus and amplitude of the complex number z=2−i(2tan5π8)z=2-i\left(2 \tan \frac{5 \pi}{8}\right)z=2−i(2tan85π), then (r,θ)(\mathrm{r}, \theta)(r,θ) is equal toA(2sec11π8,11π8)\left(2 \sec \frac{11 \pi}{8}, \frac{11 \pi}{8}\right)(2sec811π,811π)B(2sec3π8,3π8)\left(2 \sec \frac{3 \pi}{8}, \frac{3 \pi}{8}\right)(2sec83π,83π)C(2sec5π8,3π8)\left(2 \sec \frac{5 \pi}{8}, \frac{3 \pi}{8}\right)(2sec85π,83π)D(2sec3π8,5π8)\left(2 \sec \frac{3 \pi}{8}, \frac{5 \pi}{8}\right)(2sec83π,85π)Check answerSkip