# How do you write the trigonometric form of 4?

##### 1 Answer

The trigonometric form of a complex number is

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

where

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

and

$\theta = {\tan}^{-} 1 \left(\frac{y}{x}\right)$

For $4$ we have that

$z = 4 = 4 + 0 \cdot i$ hence $x = 4$ ,$y = 0$

therefore $r = 4$ and $\theta = 0$

Hence in trigonometric form

$z = 4 \cdot \left(\cos 0 + i \sin 0\right)$