Question

How do you write the following in trigonometric form and perform the operation given `4(1-sqrt3i)`?

Answer 1

The trigonometric form is `z=8(cos(-pi/3)+isin(-pi/3))`

Explanation:

let `z=4(1-isqrt3)`
The trigonometric form is `z=r(costheta+isintheta)`
Rewriting `z=8(1/2-(isqrt3)/2)`

Comparing this to the first equation
`costheta=1/2` and `sintheta=-sqrt3/2`
So we are in the 4th quadrant
and `theta=-pi/3`

So the trigonometric form is `z=8(cos(-pi/3)+isin(-pi/3))`