Question

How can you use trigonometric functions to simplify `16 e^( ( pi)/3 i )` into a non-exponential complex number?

Answer 1

`8+8sqrt3i`

Explanation:

We can use the identity `re^(itheta)=rcostheta+irsintheta`

Hence, `16e^(pi/3i)=16cos(pi/3)+16sin(pi/3)i`

= `16xx1/2+16xxsqrt3/2i`

= `8+8sqrt3i`