# How do you find the trigonometric form of a complex number?

Jun 14, 2018

As detailed below.

#### Explanation:

Trigonometric Form of a Complex Number. The trigonometric form of a complex number z = a + bi is. z = r(cos θ + i sin θ), where r = |a + bi| is the modulus of z, and tan θ = b. a.

Let the complex number be $z = \left(x + i y\right)$

Polar form is $\left(r , \theta\right)$

$r = | \sqrt{{x}^{2} + {y}^{2}} |$

$\theta = \arctan \left(\frac{y}{x}\right)$

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