Question

Convert the complex number 2 - 2root3 into its polar representation. ??

Answer 1

@SolomonZelman @perl @Kainui

Answer 2

@OOOPS @Oooky

Answer 3

@ganeshie8

Answer 4

\((2, -2\sqrt3)\), right?

Answer 5

first off, x =2, y = -2root3, hence x^2+y^2 =r^2 =?

Answer 6

I guide you how to find it out, I don't do your homework

Answer 7

answer me step by step, you can get it, it is not hard
x^2 +y^2 =?

Answer 8

http://www.wolframalpha.com/widgets/view.jsp?id=47e6fd9e600778e368177b1edd70b025 try using this calculator

Answer 9

right ok so x^2 is 4 and
y^2 = 12?

Answer 10

@Oooky on test, we don't have math tools

Answer 11

so r = 4?

Answer 12

yup

Answer 13

It was for future reference :P

Answer 14

now, take r out by factor (2, -2root3) what do you get?

Answer 15

ok, may be this is hard for you, I guide you this :)

Answer 16

yeah how do i do that haha

Answer 17

good luck :)))

Answer 18

for x =2 , do you agree that 2 = 4*\(\dfrac{2}{4}\)

Answer 19

hence if I take 4 out, then the rest is 1/2, right?

Answer 20

yup i got that

Answer 21

do the same with y, we have y = \(-2\sqrt 3= 4*-2\sqrt3/4 \) if I take 4 out, I have the rest is \(-\dfrac{\sqrt 3}{2}\), right?

Answer 22

so far, I have \(4(\dfrac{1}{2}, -\dfrac{\sqrt3}{2}) \) got me so far?
I just take 4 out from the original (x, y)

Answer 23

yeah I follow that

Answer 24

cos ??= 1/2?

Answer 25

pi/3?

Answer 26

oh, there is an easier way to do, hihihi... but by mistake, I go on this way. go ahead or go other way?? hahahah....
but the step to get r is perfect,

Answer 27

either way haha

Answer 28

ok, \(tan \theta =\dfrac{y}{x}\), just put the original x, y in to get tan

Answer 29

I get tan theta = root 3

Answer 30

-root 3, right? not root 3

Answer 31

that's pi/3

Answer 32

oh right so -pi/3

Answer 33

positive one, please

Answer 34

so is it A?

Answer 35

\[\sqrt[4]{3} \cos(60) = i \sin(60)\]