How can you use trigonometric functions to simplify $12 e^( ( pi)/3 i )$ into a non-exponential complex number?

Question

1283 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-06-29T08:35:30

$12e^(pi/3i)=6+6sqrt3i$

A complex number in polar form can be written in two ways -

(a) $re^(itheta)$ or (b) $rcostheta+irsintheta$

Hence $12e^(pi/3i)=12cos(pi/3)+i12sin(pi/3)$

= $12xx1/2+ixx12xxsqrt3/2$

= $6+6sqrt3i$

How can you use trigonometric functions to simplify 12 e^( ( pi)/3 i ) 12 e^( ( pi)/3 i ) into a non-exponential complex number?