Complex number solution for theta

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June 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
June 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.
June 6th 2008, 07:54 AM
taurus

i still dont get it?
June 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: . $\theta \;=\;\frac{4\pi}{3}\,\text{ or }\,\text{-}\,\frac{2\pi}{3}$
June 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?

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