How do you write the complex number in standard form 3/4(cos315+isin315)?

Sep 8, 2016

$\frac{3 \sqrt{2}}{8} - \frac{3 \sqrt{2}}{8} i$

Explanation:

The first step is to evaluate the $\textcolor{b l u e}{\text{trigonometric part}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\cos {315}^{\circ} = \cos {45}^{\circ} = \frac{1}{\sqrt{2}}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\sin {315}^{\circ} = - \sin {45}^{\circ} = \frac{1}{\sqrt{2}}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\Rightarrow \frac{3}{4} \left(\frac{1}{\sqrt{2}} - \frac{1}{\sqrt{2}} i\right) = \frac{3}{4 \sqrt{2}} \left(1 - i\right)$

Rationalising the denominator to 'tidy up'

$= \frac{3 \sqrt{2}}{8} \left(1 - i\right) = \frac{3 \sqrt{2}}{8} - \frac{3 \sqrt{2}}{8} i \leftarrow \text{ in standard form}$