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How do you multiply #e^(( 4 pi )/ 3 i) * e^( pi/2 i ) # in trigonometric form?

Answer 1

Asher Friedman

#\frac{\sqrt3-i}{2}#

#e^{{4\pi}/3i}\cdot e^{\pi/2i}#

#=e^{{4\pi}/3i+\pi/2i}#

#=e^{i({4\pi}/3+\pi/2)}#

#=e^{{11\pi}/6i}#

#=\cos({11\pi}/6)+i\sin({11\pi}/6)#

#=\cos(2\pi-{\pi}/6)+i\sin(2\pi-{\pi}/6)#

#=\cos({\pi}/6)-i\sin({\pi}/6)#

#=\sqrt3/2-i 1/2#

#=\frac{\sqrt3-i}{2}#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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