# Complex number solution for theta

• Jun 6th 2008, 07:33 AM
taurus
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
• Jun 6th 2008, 07:47 AM
TheEmptySet
Quote:

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.
• Jun 6th 2008, 07:54 AM
taurus
i still dont get it?
• Jun 6th 2008, 08:12 AM
Soroban
Hello, taurus!

Did you make a sketch?

Quote:

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

• Jun 6th 2008, 08:45 AM
taurus
How did u get the -2pi/3?

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