Question

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))

Answer 1

I am thinking that the answer would be C. Having some trouble however.

Answer 2

\[z _{1}=r _{1} \left( \cos \theta1+ \iota \sin \theta1 \right)=r _{1}e ^{i \theta1}\]
\[z _{2}=r2\left( \cos \theta2+\iota \sin \theta2 \right)=r2e ^{i \theta2}\]
\[z _{1}*z _{2}=r1*r2e ^{i \left( \theta1+\theta2 \right)}\]
\[=r1*r2\left( \cos \left( \theta1+\theta2 \right)+\iota \sin \left( \theta1+\theta2 \right) \right)\]

Answer 3

Oh 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.

Answer 4

correct

Answer 5

Now we have to add pi/4 and 3pi/8 which gives us cos(5pi/8) which is C! Thank you!!

Answer 6

well done

Answer 7

I wish I knew about this formula sooner hahaha! Thank you so much!

Answer 8

yw