# How do you write the complex number z = −2 − 2isqrt3  in trigonometric form?

Feb 18, 2016

As you can see this is the ${30}^{0} , {60}^{0} , {90}^{0}$ right angle triangle which happen to have $2 , \sqrt{3} , 1$ relationship between the sides.
The phasor that you were given is scale by 2. See image...
From this the magnitude of you Phasor, P:$| P | = 4$
and the direction angle is $\alpha = {240}^{0}$ see image
Thus you can write:
$P = 4 \cos 240 + i 4 \sin 240 = - 2 - i 3.46 = - 2 - i 2 \sqrt{2}$

#### Explanation:

See above it is self evident on the image...