How do you write the complex number in standard form #5(cos135+isin135)#?

1 Answer
Apr 30, 2017

Answer:

Substitute in the values for the trigonometric functions.
Distribute the radius through the parenthesis.
Swap the position of the i.

Explanation:

Given #5(cos(135^@)+isin(135^@))#

Write in the standard form, #a + bi#

The value of #cos(135^@) = -sqrt(2)/2#
The value of #sin(135^@)=sqrt(2)/2#

Substitute these values into the given form:

#5(-sqrt(2)/2+isqrt(2)/2)#

Distribute the 5 through the parenthesis

#(-5sqrt(2))/2+i(5sqrt(2))/2#

Swap the position of the i:

#(-5sqrt(2))/2+(5sqrt(2))/2i" "larr# this is the standard form.