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divide 9(cos5pi/4+i sin5pi/4)/3(cos pi+i sin pi)

 Mar 11, 2018
 #1
avatar+102466 
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divide 9(cos5pi/4+i sin5pi/4)/3(cos pi+i sin pi)

 

\(9(cos5pi/4+i sin5pi/4)/3(cos pi+i sin pi)\\ =\frac{9e^{(5\pi/4)i}}{3e^{(\pi/4)i}}\\ =\frac{3e^{(5\pi/4)i}}{e^{(\pi/4)i}}\\ =3e^{(5\pi/4)i-(\pi/4)i}\\ =3e^{(4\pi/4)i}\\ =3e^{\pi i}\\ =3(cos\pi+i sin\pi)\\ =3(-1+0)\\ =-3\)

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 Mar 11, 2018
 #2
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 Mar 12, 2018

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