How do you evaluate # e^( ( pi)/4 i) - e^( ( 7 pi)/6 i)# using trigonometric functions?

1 Answer
Feb 19, 2016

Pl use Euler's formula to evalute

Explanation:

Euler's formula is #e^(ix) = cosx+isinx #
So #e^(pi/4i)#-#e^(7pi/6i)#
# = cos(pi/4)+isin(pi/4) - ( cos(7pi/6)+isin(7pi/6))#
# = cos(pi/4)-cos(7pi/6)) +i ( sin(pi/4-sin(7pi/6))#
# = cos(pi/4)-cos(pi+pi/6)) +i ( sin(pi/4-sin(pi+pi/6))#
# = cos(pi/4)+cos(pi/6)) +i ( sin(pi/4+sin(pi/6))#
# = 1/sqrt2+sqrt3/2+i(1/sqrt2+1/2)#

please check it and give feed back