Question

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))

Answer 1

Have you considered multiplying the leading coefficients and adding the angles?

Answer 2

so 3*7?

Answer 3

Now, the second part.

Answer 4

multiply pi/4*pi/4?

Answer 5

Read my first post.

Answer 6

Add pi/4+pi/4?

Answer 7

Why would you do that?

When you came up with 3*7, you took a value from each of z1 and z2. You should do the same with the addition.

Answer 8

you add 3 and 7? is that what you're saying?

Answer 9

No, Please don't reverse correct things you did already.

Multiply the leading constants: 3*7 -- Done. Don't change that.
Add the angles: ?? + ??

Answer 10

ok I think I understand I use the unit circle to figure out the angle then I add?

Answer 11

?? The angles are given. Why do you need a unit circle? \(\dfrac{\pi}{4}+\dfrac{3\pi}{8}\) -- Go!

Answer 12

5pi/8

Answer 13

Now, if this happens to be greater than \(2\pi\), you might need that Unit Circle.

What is your final answer? You have all the pieces.

Answer 14

So do I do 21cos(5pi/8)+i sin(5pi/8) ?

Answer 15

Not quite. The parentheses are not optional.

Answer 16

21(cos(5pi/8)+i sin(5pi/8))

Answer 17

Perfect.

Answer 18

okay let me solve

Answer 19

Solve what? You are done. Move on to the next one.

Answer 20

oh that's it?

Answer 21

That's all there is to it. :-)

Answer 22

thanks