How do you evaluate # e^( (3 pi)/2 i) - e^( ( pi)/3 i)# using trigonometric functions?
1 Answer
Feb 26, 2017
Use Euler's identity:
#e^(ix) = cosx + isinx#
Thus:
#e^((3pi)/2i) - e^(pi/3i)#
#= cos((3pi)/2) + isin((3pi)/2) - (cos(pi/3) + isin(pi/3))#
#= cancel(cos((3pi)/2))^(0) + isin((3pi)/2) - cos(pi/3) - isin(pi/3)#
#= -i - 1/2 - sqrt3/2i#
#= color(blue)(-1/2 + (-1 - sqrt3/2)i)#
So, for the form
