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

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Answer 1 · 2016-07-05T15:48:58

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

Recall Euler's formula:

$e^(itheta) = costheta + isintheta$

Hence

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

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