How do you multiply e^(( 5 pi )/ 4 i) * e^( pi/2 i ) in trigonometric form?

1 Answer
Apr 13, 2016

e^((5pi/4)i)*e^((pi/2)i)=-1/sqrt2-i1/sqrt2

Explanation:

A complex number can be written in polar form in two ways - either as r*e^(itheta) or as rcostheta+irsintheta.

Hence,

e^((5pi/4)i)=cos(5pi/4)+isin(5pi/4) and

e^((pi/2)i)=cos(pi/2)+isin(pi/2)

Hence, e^((5pi/4)i)*e^((pi/2)i)

= (cos(5pi/4)+isin(5pi/4))*(cos(pi/2)+isin(pi/2))

= (cos(5pi/4)+isin(5pi/4))*(0+i)

as cos(pi/2)=0 and sin(pi/2)=1

= (icos(5pi/4)+i^2sin(5pi/4))

= -sin(5pi/4)+icos(5pi/4)

= -1/sqrt2-i1/sqrt2