How do you multiply #e^(( 3 pi )/ 4 i) * e^( 3 pi/2 i ) # in trigonometric form?
1 Answer
Mar 9, 2016
Explanation:
From the identity
#e^{itheta} -= cos(theta) + i sin(theta)#
We write
#e^{i{3pi}/4} * e^{i{3pi}/2} = (cos({3pi}/4) + i sin({3pi}/4)) * (cos({3pi}/2) + i sin({3pi}/2))#
#= (-1/sqrt2 + i (1/sqrt2)) * (0 + i (-1))#
#= 1/sqrt2*(-1 + i) * (- i)#
#= 1/sqrt2*(i + 1)#
#= 1/sqrt2+ i/sqrt2#
