Question

How can you use trigonometric functions to simplify `2 e^( ( 5 pi)/3 i )` into a non-exponential complex number?

Answer 1

`2 [cos((5pi)/3) + isin((5pi)/3) ]`

Explanation:

Using Euler's identity , which states :

`re^(theta i) = r ( costheta + isintheta )`

here r = 2 and `theta = (5pi)/3`

`rArr 2e^(5pi/3 i) = 2[cos((5pi)/3) + isin((5pi)/3) ]`