# How do you write the trigonometric form of -6?

Nov 7, 2016

I found: $z = 6 \left[\cos \left(\pi\right) + i \sin \left(\pi\right)\right]$

#### Explanation:

We can "see" this number ($z = - 6$) on the Real axis on a complex plane:

We need the angle $\theta$ and the modulus (length) to define the characteristics of our number in trig form as:
$z = \text{modulus} \left[\cos \left(\theta\right) + i \sin \left(\theta\right)\right]$
observing our complex plane we see that:
modulus$= 6$
$\theta = \pi = {180}^{\circ}$
so ve get:
$z = 6 \left[\cos \left(\pi\right) + i \sin \left(\pi\right)\right]$