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How can you use trigonometric functions to simplify # 8 e^( ( pi)/8 i ) # into a non-exponential complex number?

1 Answer

Apr 16, 2016

#7.392 + 3.064i#

Explanation:

According to Euler's formula,

#e^(ix) = cosx + isinx#.

Inserting the value #x = pi/8# from the equation, then

#e^(pi/8i) = cos(pi/8) + isin(pi/8)#
# = cos22.5 + isin22.5#
# = 0.924 + 0.383i#.

Multiplying all this by #8# as in the question, and

#8e^(pi/8i) = 7.392 + 3.064i#

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