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

1 Answer
Sep 8, 2016

Answer:

#(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"#