Question

What is the trigonometric form of `(-2+9i)`?

Answer 1

`sqrt(85)(cos(tan^-1(-9/2))+isin(tan^-1(-9/2)))`

Explanation:

`(-2+9i)`

`rcos(theta)=-2`
`rsin(thea) = 9`

Squaring both and adding

`r^2cos^2(theta) = 4`
`r^2sin^2(theta) = 81`

`r^2cos^2(theta)+r^2sin^2(theta) = 4+81`
`r^2(cos^2(theta)+sin^2(theta))=85`
`r^2=85`
`r=sqrt(85)`

`rsin(theta)/rcos(theta) = 9/-2`
`tan(theta) = -9/2`

`theta = tan^-1(-9/2)`

The complex number in trigonometric form is

`sqrt(85)(cos(tan^-1(-9/2))+isin(tan^-1(-9/2)))`