How do you evaluate # 2 e^( ( 23 pi)/8 i) - e^( ( 19 pi)/8 i)# using trigonometric functions?

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Answer 1 · 2018-07-17T09:22:58

#color(maroon)(2e^((23 pi)/(8) i) - e^(( 19pi)/8 i) ~~ -2.2305 - 0.1585 i#

# 2e^((23 pi)/(8) i) - e^(( 19pi)/8 i)#

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

#:. 2e^((23 pi)/(8) i) = 2(cos ((23 pi)/8)+ i sin ((23 pi)/8))#

# = - 1.8478 + 0.7654 i #, II Quadrant

#:. e^((19 pi)/8 i) = (cos ((19pi)/8)+ i sin ((19pi)/8)#

#0.3827 + 0.9239 i#, I Quadrant

#:. 2e^((23 pi)/(8) i) - e^(( 19pi)/8 i)#

#~~( -1.8478 + 0.7654 i ) - ( 0.3827 + 0.9239 i)#

#color(maroon)(2e^((23 pi)/(8) i) - e^(( 19pi)/8 i) ~~ -2.2305 - 0.1585 i#