Complex number solution for theta

**taurus** · June 6th 2008, 07:33 AM

Given z = -1 - sqrt(3)i

What is the value of theta?
I got pi/3 but that is not right, the correct answer is -2pi/3

Thanks

**TheEmptySet** · June 6th 2008, 07:47 AM

Originally Posted by taurus

Given z = -1 - sqrt(3)i

What is the value of theta?
I got pi/3 but that is not right, the correct answer is -2pi/3

Thanks

$\frac{\pi}{3}$ is your reference angle

Think of -1 as being the x coordinate and $-\sqrt{3}$ as your y

This you put the point in quadrant III rotated down $\frac{\pi}{3}$ from the negative x-axis.

I hope this helps.

**taurus** · June 6th 2008, 07:54 AM

i still dont get it?

**Soroban** · June 6th 2008, 08:12 AM

Hello, taurus!

Did you make a sketch?

Given: . $z \:= \:-1 - i\sqrt{3}$

What is the value of $\theta$ ?

Code:

                |
                |
                |
            -1  |
      - - + - - * - - - -
          :    /|
        _ :   / |
      -√3 :  /  |
          : /   |
          :/    |
          *     |

Can you see that the angle is: . $\theta \;=\;240^o\,\text{ or }\,\text{-}120^o$ ?

In radians: . $\theta \;=\;\frac{4\pi}{3}\,\text{ or }\,\text{-}\,\frac{2\pi}{3}$

**taurus** · June 6th 2008, 08:45 AM

How did u get the -2pi/3?

i did this:
-120*pi/360
=pi/3 which is not right?

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