Question

How do you write the complex number in trigonometric form `-8+3i`?

Answer 1

The trigonometric form is `=2.92 (cos(159.4^@)+isin(159.4^@))=2.92e^(159.4^@i)`

Explanation:

Our complex number is

`z=-8+3i`

The trigonometric form is

()()`z=r(costheta+isintheta)`

If our complex number is `z=a+ib`

`r=|z|=sqrt(a^2+b^2)`

And

`costheta=a/|z|` and

`sintheta=b/|z|`

Therefore,

`|z|=sqrt((-8)^2+3^2)=sqrt(64+9)=sqrt73=2.92`

`costheta=-8/sqrt73`

`sintheta=3/sqrt73`

We are in the Quadrant `II`

`Theta=159.4^@`

The trigonometric form is

`z=2.92 (cos(159.4^@)+isin(159.4^@))=2.92e^(159.4^@i)`