Complex solution to cos x = 2?

[johann1301]

Are there any complex solutions to cos x = 2?

 

[Char. Limit]

Yes.

 

[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.

 

[johann1301]

Thanks!