Thread: Principle Argument of a Complex number?

1. Principle Argument of a Complex number?

Alright all ive got the complex number

(8)^1/2 - i (24)^1/2.

So i put Tan theta = root 24 / root 8

I get theta as Pi/3.

Is this the principle agrument?

2. Originally Posted by simpleas123
Alright all ive got the complex number
(8)^1/2 - i (24)^1/2.
So i put Tan theta = root 24 / root 8
I get theta as Pi/3.
Is this the principle agrument?
No it is not.
Note that if $x>0$ then $\arg(x+yi)=\arctan\left(\frac{y}{x}\right)$.
In this case $y=-\sqrt{24}$ so $\left(\frac{-\pi}{3}\right)$.