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Complex solution to cos x = 2?

  1. Jul 22, 2014 #1
    Are there any complex solutions to cos x = 2?
     
  2. jcsd
  3. Jul 22, 2014 #2

    Char. Limit

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  4. Jul 22, 2014 #3

    Char. Limit

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

    [tex]cos(x) = \frac{e^{i x} + e^{- i x}}{2}[/tex]

    Set the right side equal to 2, and solve for x. Hint, it's going to involve a quadratic equation in e^x.
     
  5. Jul 22, 2014 #4
    Thanks!
     
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