# How do you write the complex number in trigonometric form 4?

Aug 15, 2016

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

#### Explanation:

To express a complex number in trigonometric form.

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{z = x + y i = r \left(\cos \theta + i \sin \theta\right)} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder}}$

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{r = \sqrt{{x}^{2} + {y}^{2}}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\theta = {\tan}^{-} 1 \left(\frac{y}{x}\right)} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

consider $z = 4 = 4 + 0 i$

here x = 4 and y = 0

$\Rightarrow r = \sqrt{{4}^{2} + {0}^{2}} = 4$

and $\theta = {\tan}^{-} 1 \left(\frac{0}{4}\right) = {\tan}^{-} 1 \left(0\right) = 0$

$\Rightarrow z = 4 = 4 \left(\cos 0 + i \sin 0\right) \text{ in trigonometric form}$