How do you evaluate # e^( (3 pi)/2 i) - e^( ( pi)/2 i)# using trigonometric functions?

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How do you evaluate # e^( (3 pi)/2 i) - e^( ( pi)/2 i)# using trigonometric functions?

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Answer 1 · 2016-04-04T07:20:58

#-2i#

Explanation:

#e^(ix)=cos x + i sin x#.
#cos(3pi/2)=cos(pi/2)=0#
#sin(3pi/2)=sin(pi+pi/2)=-sin(pi/2)=-1# and #sin(pi/2)=1#
So the expression simplifies to #-i-i=-2i#.(

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How do you evaluate # e^( (3 pi)/2 i) - e^( ( pi)/2 i)# using trigonometric functions?

1 Answer

Explanation:

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