How do you evaluate # e^( ( pi)/4 i) - e^( ( 7 pi)/3 i)# using trigonometric functions?
1 Answer
Jul 13, 2018
Euler's Formula states that
#e^(icolor(red)theta) = coscolor(red)theta+isincolor(red)theta#
Which is the trigonometric form of a complex number. Hence,
#e^(icolor(red)(pi/4))=cos(color(red)(pi/4)) +isin(color(red)(pi/4))=sqrt2/2+isqrt2/2#
#e^(icolor(red)((7pi)/3))=cos(color(red)((7pi)/3)) + isin(color(red)((7pi)/3))#
#=cos(2pi+pi/3)+isin(2pi+pi/3)#
#=cos(pi/3) + i sin(pi/3)#
#=1/2+isqrt3/2#
#=(sqrt2/2-1/2)+i(sqrt2/2-sqrt3/2)#
