How do you multiply #e^((11pi )/ 12 ) * e^( pi i ) # in trigonometric form?

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Answer 1 · 2018-07-27T13:12:33

#color(purple)(e^((11 pi)/(12) i) * e^(( pi) i) ~~ 0.9659 - 0.2588 i#, IV Quadrant.

# e^((11 pi)/(12) i) * e^(( pi) i)#

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

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

# = - 0.9659 + 0.2588 i #, II Quadrant

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

# = -1, # II Quadrant.

#:. e^((11 pi)/(12) i) * e^(( pi) i)#

#~~( - 0.9659 + 0.2588 i ) * ( -1 )#

#~~ 0.9659 - 0.2588 i #

#color(purple)(e^((11 pi)/(12) i) * e^(( pi) i) ~~ 0.9659 - 0.2588 i#, IV Quadrant.

Verification :

#=> e^i (((11pi)/12) + (pi))#

#=> e^i ((23pi)/12)#

#=> cos ((23pi)/12) + i sin ((23pi)/12)#

#=> 0.9659 - 0.2588i#, IV Quadrant.