How do you write the complex number in trigonometric form -5i?

Feb 26, 2017

The answer is $= 5 \left(\cos \left(- \frac{1}{2} \pi\right) + i \sin \left(- \frac{1}{2} \pi\right)\right)$

Explanation:

The trigonometric form of a complex number is

$z = r \left(\cos \theta + i \sin \theta\right)$

Here, we have

$z = - 5 i$

Therefore,

$r = 5$

$\cos \theta = 0$

$\sin \theta = - 1$

So, $\theta = - \frac{1}{2} \pi$

$z = 5 \left(\cos \left(- \frac{1}{2} \pi\right) + i \sin \left(- \frac{1}{2} \pi\right)\right)$

$= 5 {e}^{- \frac{1}{2} i \pi}$