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How can you use trigonometric functions to simplify # 3 e^( ( pi)/4 i ) # into a non-exponential complex number?

1 Answer

Jul 5, 2016

#3e^(pi/4i) = (3sqrt(2))/2[1+i]#

Explanation:

Recall Euler's formula:

#e^(itheta) = costheta + isintheta#

Hence

#3e^(pi/4i) = 3[cos(pi/4)+isin(pi/4)] = 3[(sqrt(2))/2 + (sqrt(2))/2i]#

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