Question

How do you write the trigonometric form in complex form `6(cos((5pi)/6)+isin((5pi)/6)))`?

Answer 1

THe complex form is `-3sqrt3+3i`

Explanation:

The trigonometric form is `z=r(costheta+isintheta)`
The complex form is `z=a+ib`
so we have to put the values of `costheta` and `sintheta`
`cos((5pi)/6)=-cos( pi/6)=-sqrt3/2`
and `sin((5pi)/6)=sin(pi/6)=1/2`

So we have `z=6((-sqrt3/2)+i/2)=-3sqrt3+3i`