How do you write the complex number in standard form 34(cos315+isin315)?

shangokm

Answered question

2022-01-30

How do you write the complex number in standard form $\frac{3}{4}(\mathrm{cos}315+i\mathrm{sin}315)$?

Answer & Explanation

Georgia Ingram

Beginner2022-01-31Added 11 answers

The first step is to evaluate the trigonometric part
Reminder $\mathrm{cos}315}^{\circ}={\mathrm{cos}45}^{\circ}=\frac{1}{\sqrt{2}$ $\mathrm{sin}315}^{\circ}=-{\mathrm{sin}45}^{\circ}=\frac{1}{\sqrt{2}$ $\Rightarrow \frac{3}{4}(\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}i)=\frac{3}{4\sqrt{2}}(1-i)$
Rationalising the denominator to tidy