Complex solution to cos x = 2?

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Discussion Overview

The discussion centers around the question of whether there are complex solutions to the equation cos x = 2, exploring the implications and methods for finding such solutions.

Discussion Character

  • Exploratory, Technical explanation

Main Points Raised

  • One participant questions the existence of complex solutions to cos x = 2.
  • Another participant asserts that there are indeed solutions.
  • A further contribution suggests using an alternate definition of the cosine function involving exponential functions to find the solutions, indicating that this will lead to a quadratic equation in e^x.
  • A participant expresses gratitude for the information provided.

Areas of Agreement / Disagreement

There is a disagreement regarding the existence of complex solutions, with some participants asserting their existence while others have not yet provided a counterpoint.

Contextual Notes

The discussion does not clarify the specific steps or assumptions involved in solving the quadratic equation mentioned, leaving some mathematical details unresolved.

johann1301
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Are there any complex solutions to cos x = 2?
 
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Yes.
 
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.
 
Thanks!
 

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