Question 563177
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I'm going to assume you meant *[tex \Large \cos(45^\circ)] and *[tex \Large \sin(45^\circ)], otherwise this problem is a big ugly mess.


Use the unit circle:


<img src="http://www.math.ucsd.edu/~jarmel/math4c/Unit_Circle_Angles.png">


to determine that *[tex \Large \cos(45^\circ)\ =\ \sin(45^\circ)\ =\ \frac{\sqrt{2}}{2}]. 


Substitute and the use FOIL.  Don't forget that *[tex \Large i\ \times\ i\ =\ -1].  Collect terms.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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