# How do you write the complex number in standard form 5(cos135+isin135)?

Apr 30, 2017

Substitute in the values for the trigonometric functions.
Distribute the radius through the parenthesis.
Swap the position of the i.

#### Explanation:

Given $5 \left(\cos \left({135}^{\circ}\right) + i \sin \left({135}^{\circ}\right)\right)$

Write in the standard form, $a + b i$

The value of $\cos \left({135}^{\circ}\right) = - \frac{\sqrt{2}}{2}$
The value of $\sin \left({135}^{\circ}\right) = \frac{\sqrt{2}}{2}$

Substitute these values into the given form:

$5 \left(- \frac{\sqrt{2}}{2} + i \frac{\sqrt{2}}{2}\right)$

Distribute the 5 through the parenthesis

$\frac{- 5 \sqrt{2}}{2} + i \frac{5 \sqrt{2}}{2}$

Swap the position of the i:

$\frac{- 5 \sqrt{2}}{2} + \frac{5 \sqrt{2}}{2} i \text{ } \leftarrow$ this is the standard form.