Answered: "How do you write the complex number in..." - Plainmath

shangokm

Answered question

2022-01-30

How do you write the complex number in standard form

\frac{3}{4} (\cos 315 + i \sin 315)

?

Answer & Explanation

Georgia Ingram

Beginner2022-01-31Added 11 answers

The first step is to evaluate the trigonometric part
Reminder

{\cos 315}^{\circ} = {\cos 45}^{\circ} = \frac{1}{\sqrt{2}}

{\sin 315}^{\circ} = - {\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

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