Question

Trig: Which complex number's graph is shown?

Answer 1

ANSWER

$2 \sqrt{2} ( \cos( \frac{7\pi}{4} + i \sin( \frac{7\pi}{4} ) )$

EXPLANATION

The complex number shown has coordinates (2,-2)

or

$z = 2 - 2i$

The modulus is

$|z| = \sqrt{ {2}^{2} + {( - 2)}^{2} }$

$|z| = \sqrt{ 8} = 2 \sqrt{2}$

The argument is

$\theta= \tan^{ - 1} ( \frac{ - 2}{2} )$

$\theta= \tan^{ - 1} ( -1) = \frac{7\pi}{4}$

The polar form is

$2 \sqrt{2} ( \cos( \frac{7\pi}{4} + i \sin( \frac{7\pi}{4} ) )$

The first option is correct.