Question

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

Answer 1

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.