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How can you use trigonometric functions to simplify # 2 e^( ( pi)/4 i ) # into a non-exponential complex number?

1 Answer

Dec 30, 2015

#sqrt(2) (1+i)#

Explanation:

#e^(i Theta) = cos(Theta) + i sin(Theta)#

Therefore:
#2e^(pi/4 i) = 2(cos(pi/4) + i sin(pi/4))#

= #2(1/sqrt(2) + i 1/sqrt(2))#
= #2((sqrt(2) + i sqrt(2))/2)#
=#sqrt(2) (1 + i)#

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