Question

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

Answer 1

`(3sqrt2)/8-(3sqrt2)/8 i`

Explanation:

The first step is to evaluate the `color(blue)"trigonometric part"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(cos315^@=cos45^@=1/sqrt2)color(white)(a/a)|)))`

`color(red)(bar(ul(|color(white)(a/a)color(black)(sin315^@=-sin45^@=1/sqrt2)color(white)(a/a)|)))`

`rArr3/4(1/sqrt2-1/sqrt2 i)=3/(4sqrt2)(1-i)`

Rationalising the denominator to 'tidy up'

`=(3sqrt2)/8(1-i)=(3sqrt2)/8-(3sqrt2)/8 ilarr" in standard form"`