Question

Find the complex roots of 81[cos(3π/8) + i sin(3π/8)].

Part I: Find the fourth root of 81.

I got 3

Part II: Divide the angle in the problem by 4 to find the first argument.

I got 3(cos(3π/32) + i sin(3π/32))

Part III: Use the fact that adding 2π to the angle (3π/8) produces the same effective angle to generate the other three possible angles for the fourth roots. Be sure that your angles lie between 0 and 2π.

Part IV: Find all four of the fourth roots of the original given info. Express your answers in polar form (cosθ + i sinθ).

Answer 1

for part 3, would it just be 5π/32, 7π/32 and 9π/32?

Answer 2

what part are you stuck on?

Answer 3

part 3

Answer 4

am i correct?

Answer 5

Just a sec. I just need to start from the beginning.

Answer 6

This is just roots of unity isn't it?

Answer 7

yes

Answer 8

I can put it into polar form, I just feel like I have 3 wrong

Answer 9

is the whole equation at the very first part= z^4
and you're meant to find z?

Answer 10

no

Answer 11

just supposed to find the roots

Answer 12

Yep, I'm trying to figure out. I'm pretty much going to finish this when I get back to school. I'm just in the middle of doing this as well. I might need to think about it for a sec.

Answer 13

\[81cis \frac{ 3\pi }{ 8 }\]
Okay. You got the first part right. the second aprt right is also correct.

Answer 14

third part is wrong.

Answer 15

Wait, you just added 2pi to the numerator of 3pi/8?

Answer 16

pretty much

Answer 17

i don'y remember how to do it

Answer 18

don't*

Answer 19

You want four equal parts.

Answer 20

I'm not sure if that's correct, but I don't think part 2 is correct either. Even though it told you to divide the angle by 4, I'm confused about the third part.

Answer 21

Got it. That's it.

Answer 22

find each four of those angles like that.