Question

How do you write the trigonometric form in complex form `3/2(cos((5pi)/3)+isin((5pi)/3)))`?

Answer 1

`3/2(cos((5pi)/3)+isin((5pi)/3))=3/4-i(3sqrt3)/4`

Explanation:

As `cos((5pi)/3)=cos(2pi-pi/3)=cos(-pi/3)=cos(pi/3)=1/2`

and `sin((5pi)/3)=sin(2pi-pi/3)=sin(-pi/3)=-sin(pi/3)=-sqrt3/2`

Hence `3/2(cos((5pi)/3)+isin((5pi)/3))`

= `3/2(1/2-isqrt3/2)`

= `3/4-i(3sqrt3)/4`