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anonymous
 one year ago
Stuck on complex problem!
Find the product of the complex numbers. Express your answer in trigonometric form.
z1 = 3 (cos(pi/4) + i sin(pi/4))
z2 = 7 (cos(3pi/8) + i sin(3pi/8))
A. 3/7 (cos(5pi/8) + i sin(5pi/8))
B. 3/7 (cos(pi/8) + i sin(pi/8))
C. 21(cos(5pi/8) + i sin(5pi/8))
D. 21(cos(pi/8) + i sin(pi/8))
anonymous
 one year ago
Stuck on complex problem! Find the product of the complex numbers. Express your answer in trigonometric form. z1 = 3 (cos(pi/4) + i sin(pi/4)) z2 = 7 (cos(3pi/8) + i sin(3pi/8)) A. 3/7 (cos(5pi/8) + i sin(5pi/8)) B. 3/7 (cos(pi/8) + i sin(pi/8)) C. 21(cos(5pi/8) + i sin(5pi/8)) D. 21(cos(pi/8) + i sin(pi/8))

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I am thinking that the answer would be C. Having some trouble however.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[z _{1}=r _{1} \left( \cos \theta1+ \iota \sin \theta1 \right)=r _{1}e ^{i \theta1}\] \[z _{2}=r2\left( \cos \theta2+\iota \sin \theta2 \right)=r2e ^{i \theta2}\] \[z _{1}*z _{2}=r1*r2e ^{i \left( \theta1+\theta2 \right)}\] \[=r1*r2\left( \cos \left( \theta1+\theta2 \right)+\iota \sin \left( \theta1+\theta2 \right) \right)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh ok! So from looking at the formula, I can see right away that the answer would not be A or B because we multiply 3 by 7.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now we have to add pi/4 and 3pi/8 which gives us cos(5pi/8) which is C! Thank you!!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I wish I knew about this formula sooner hahaha! Thank you so much!
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