SOLUTION: Multiply 8(cos 35� + i sin 35�) and 8(cos 50� + i sin 50�). Can you please explain how to do this step by step? Thank You.

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Question 996072: Multiply 8(cos 35� + i sin 35�) and 8(cos 50� + i sin 50�). Can you please explain how to do this step by step? Thank You.
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Rule:
If
z1 = r1 * [ cos(theta1)+i*sin(theta1) ]
z2 = r2 * [ cos(theta2)+i*sin(theta2) ]
Then
z1*z2 = (r1*r2) * [ cos(theta1+theta2)+i*sin(theta1+theta2) ]

In plain English:
multiply the r values out front; add the angles

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In this case,

z1 = 8(cos 35� + i sin 35�)
z2 = 8(cos 50� + i sin 50�)

Using the rule above, we get
z1*z2 = (8*8)* [ cos(35�+50�) + i*sin(35�+50�) ]
z1*z2 = 64 * [cos(85�) + i*sin(85�)]

So the final answer is 64 * [cos(85�) + i*sin(85�)]