How do you evaluate # e^( ( 15 pi)/8 i) - e^( ( 11 pi)/12 i)# using trigonometric functions?

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Answer 1 · 2018-07-17T09:32:46

#color(magenta)(e^((15 pi)/(8) i) - e^(( 11pi)/12 i) ~~ -0.042 + -0.1239 i#

# e^((15 pi)/(8) i) - e^(( 11pi)/12 i)#

#e^(i theta) = cos theta +i sin theta#

#:. e^((15 pi)/(8) i) = (cos (15 pi)/(8)+ i (sin 15 pi)/(8))#

# = 0.9239 - 0.3827 i #, IV Quadrant

#:. e^(( 11pi)/12 i) = (cos ((11pi)/12)+ i sin ((11pi)/12))#

# ~~ -0.9659 + 0.2588 i#, II Quadrant

#:. e^((15 pi)/(8) i) - e^(( 11pi)/12 i)#

#~~( 0.9239 - 0.3827 i ) - ( -0.9659 + 0.2588 i)#

#color(magenta)(e^((15 pi)/(8) i) - e^(( 11pi)/12 i) ~~ -0.042 + -0.1239 i#