# Thread: Complex number solution for theta

1. ## Complex number solution for theta

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

2. 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.

3. i still dont get it?

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

5. How did u get the -2pi/3?

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