Question

Find the fourth roots of the complex number " z1 = 1 + √3 * i ". http://tinypic.com/r/2cmox3l/5

Part I: Write z1 in polar form.
Part II: Find the modulus of the roots of z1.
Part III: Find the four angles that define the fourth roots of the number z1.
Part IV: What are the fourth roots of the equation " z1 = √3 + i ".

Answer 1

CORRECT?

Part I:
a = 1
b = sqrt(3)

Part II:
sqrt(a^2 + b^2) = sqrt(1 + 3) = sqrt(4) = 2

Part III:
z = 2 * (1/2 + i * sqrt(3)/2)
z = 2 * (cos(pi/3 + 2pi * k) + i * sin(pi/3 + 2pi * k))
z = 2 * (cos((pi/3) * (1 + 6k)) + i * sin((pi/3) * (1 + 6k)))
z^(1/4) = 2^(1/4) * (cos((pi/12) * (1 + 6k)) + i * sin((pi/12) * (1 + 6k)))

Part IV:
2^(1/4) * (cos(pi/12) + i * sin(pi/12))
2^(1/4) * (cos(7pi/12) + i * sin(7pi/12))
2^(1/4) * (cos(13pi/12) + i * sin(13pi/12))
2^(1/4) * (cos(19pi/12) + i * sin(19pi/12))

Answer 2

Looks fine to me.

Answer 3

@ilfy214
Hate to give ya answer 3 hours after your post, but yeah xD

Answer 4

Lolz. Yup! You were offline

Answer 5

Everyone else just pushed my Q/A aside :( lol

Answer 6

Odd O.o Yeah, wasn't home, doctors. But nah, you did it just find on your own it seems xD

Answer 7

WOO-HOO! @ybarrap are you checking too?

Answer 8

yep

Answer 9

Its so weird how you can see when someone is viewing your question... and then you can see when they pass it

Answer 10

xD yeah, makes ya wonder. Either it's:
*damn, he doesn't know either T_T*
*bleh, lazy bastard*

Answer 11

IKR! I'm like "SERIOUSLY!!! I SEE YOU! DON'T YOU DARE PASS ME!" hahah

Answer 12

There are certain problems I target more than others, but if I pass up a question it's because I'm clueless or I don't want to interrupt someone else answering.

Answer 13

Totally understand

Answer 14

But I keep all the trig review I can get, so works for me xD

Answer 15

*need
where the hell did I get "keep" from? O.o

Answer 16

Maybe because of the two "ee"s?

Answer 17

Aww, ybarrap deleted all that drawing.

Answer 18

WAIT! NO! I DIDN'T SEE @ybarrap

Answer 19

It's not something you will learn :P But it is an answer

Answer 20

I don't personally know it either, but I've seen it a bit.