How do you multiply #e^((13 pi )/ 12 ) * e^( pi/4 i ) # in trigonometric form?

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Answer 1 · 2018-07-17T07:55:26

#color(purple)(e^((13 pi)/(12) i) * e^(( pi)/4 i) ~~ -0.5 - 0.866 i#

# e^((13 pi)/(12) i) * e^(( pi)/4 i)#

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

#(3 pi)/8 ~~ 3.4034 , ( pi)/4 ~~ 0.7854#

#:. e^((13 pi)/(12) i) = (cos ((13 pi)/12)+ i sin ((13 pi)/12))#

# = - 0.9659 - 0.2588 i #, III Quadrant

#:. e^(( pi)/4 i) = (cos (pi/4)+ i sin (pi/4)#

# ~~ 0.7071 + 0.7071 i#

#:. e^((13 pi)/(12) i) * e^(( pi)/4 i)#

#~~( - 0.9659 - 0.2588 i ) * ( 0.7071 + 0.7071 i)#

#~~ -0.683 + 0.183 -0 .683 i - 0.183 i#

#color(purple)(e^((13 pi)/(12) i) * e^(( pi)/4 i) ~~ -0.5 - 0.866 i#