By: Tao Steven Zheng (鄭濤)

Problem

Determine all the values of .

Solution

To solve this problem, use Euler's formula .

Since? only has a positive imaginary component and no real component, it can be expressed as

This means

and

Since , we discover that

So we discover? is a real number! In decimal form it is approximately 0.207879576.

Since sine and cosine are periodic functions with period , for any integer , there are actually infinitely many solutions