# Complex solution to cos x = 2?

1. Jul 22, 2014

### johann1301

Are there any complex solutions to cos x = 2?

2. Jul 22, 2014

### Char. Limit

Yes.

3. Jul 22, 2014

### Char. Limit

Now for the next question. How does one find them, right? Well, you just need to take an alternate definition for the cosine function:

$$cos(x) = \frac{e^{i x} + e^{- i x}}{2}$$

Set the right side equal to 2, and solve for x. Hint, it's going to involve a quadratic equation in e^x.

4. Jul 22, 2014

Thanks!