# Thread: Difference Between an Argument and a Principle Argument in Complex Numbers?

1. ## Difference Between an Argument and a Principle Argument in Complex Numbers?

I've been trying to find a simple definition online for a while now with no luck so I thought I'd ask here. What is the difference in finding the argument of a complex number and the principle argument of a complex number.
For example given 8 + 8 sqrt(3)i I know that the argument is pi/3 and the modulus is 16, but I'm unsure about how what I need to do to find the principle argument.
Can anyone give me some help?

2. ## Re: Difference Between an Argument and a Principle Argument in Complex Numbers? Originally Posted by Daithi19 I've been trying to find a simple definition online for a while now with no luck so I thought I'd ask here. What is the difference in finding the argument of a complex number and the principle argument of a complex number.
For example given 8 + 8 sqrt(3)i I know that the argument is pi/3 and the modulus is 16, but I'm unsure about how what I need to do to find the principle argument.
Can anyone give me some help?
There are an infinite number of arguments for any complex number (because they repeat after every interval \displaystyle \displaystyle \begin{align*} 2\pi \end{align*}).

The principal argument is defined to be the argument that is in the region \displaystyle \displaystyle \begin{align*} (-\pi, \pi] \end{align*}.

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# argument and principal argument of complex numbers

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