Question

Trig: Which complex number's graph is shown?

Answer 1

The first option (the one all the way at the top)

Explanation:

a.pex

Answer 2

`2 √(2) ( \cos( (7\pi)/(4) + i \sin( (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| = √( 8) = 2 √(2)`

The argument is

`\theta= \tan^( - 1) ( ( - 2)/(2) )`

`\theta= \tan^( - 1) ( -1) = (7\pi)/(4)`

The polar form is

`2 √(2) ( \cos( (7\pi)/(4) + i \sin( (7\pi)/(4) ) )`

The first option is correct.