Question

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For questions 13 - 15, let z1=2 (cos ( pi/5)+ i sin (pi/5)) and z2=8(cos (7pi/6) + i sin (7 pi/6)). Calculate the following, keeping your answer in polar form.

|z2
As shown in this picture :https://gyazo.com/e0a0e87a836a670d65b8f01d042e18b4

Answer 1

The bar over the complex number means `complex conjugate`

http://www.mathwords.com/c/complex_conjugate.htm

Answer 2

Think about the "Reference Angle".

Answer 3

So if it worked out to -4√3-4i, the complex conjugate would be 4√3+4i ?

Answer 4

The conjugate of `-4√3-4i` would be `-4√3+4i`

Answer 5

1) Why did you change the sign of the Real Part?
2) Is that Polar Form?

Answer 6

Oh, I forgot it's the imaginary part only. I'm not sure what the polar form of the answer would be.....

Answer 7

That would be my first clue. Think about Reference Angles.

Answer 8

hint:
\[\Large -4\sqrt{3}+4i = 8\left(-\frac{\sqrt{3}}{2}+\frac{1}{2}i\right)\]

Answer 9

I factored out 8 because r = 8 for z2

Answer 10

I believe the angle given is -150 degrees, but I'm not sure where to go from there.

Answer 11

\(7\pi/6 - \pi = \pi/6\)

\(\pi - \pi/6 = 5\pi/6\)

Seriously. Reference Angles

Answer 12

z2=8(cos (7pi/6) + i sin (7 pi/6))
conjugate=-4√3+4i
r=8 and theta= 150 degrees or 5pi/6
8 (cos (5pi/6)+i sin (5pi/6)) would be the answer?

Answer 13

correct

Answer 14

Sweet, thanks a lot for helping!

Answer 15

you're welcome

Answer 16

You do not need to go through degrees.