Complex analysis

1. Oct 6, 2006

Iron Eagle

Hello everyone,

I am trying to solve this follow problem, but don't quite know how to go about getting Arg(z).

z = 6 / (1 + 4i)

I got that lzl is sqrt((6/17)^2+(-24/17)^2) but am stuck with finding Arg(z). It told me to recall that -pi < Arg(z) <= pi

Can you guys teach me how to go about finding arrrggg... this Arg(z)?

TIA.

2. Oct 6, 2006

Hurkyl

Staff Emeritus
Is there any sort of number for which you know how to compute Arg?

3. Oct 6, 2006

Iron Eagle

This Arg(z) thing is new to me, so no. I'm trying to find out what it is. Thanks.

4. Oct 6, 2006

Iron Eagle

The argument of a complex number is the angle between the positive x-axis and the line representing the complex number on an Argand diagram. It is denoted arg (z)

So Arg(z) is pretty much just the angle theta that r makes with the x-axis?

Assuming that arg(z) is not case sensitive, then is it simply arctan(-4) in this case?

Last edited: Oct 6, 2006
5. Oct 6, 2006

Hurkyl

Staff Emeritus
In this case, yes, Arg(z) = Arctan(-4). (but be wary; for some z, Arg(z) cannot equal the Arctangent of anything at all! You have to make sure you take the right value for the arctangent)

Arg/arg is case sensitive, just like other complex functions. arg is a "multi-valued function", whereas Arg picks out a specific value.

Last edited: Oct 6, 2006
6. Oct 6, 2006

Iron Eagle

Thank you so much Hurkyl... your help is much appreciated! In the meantime, I also found this page, which led me to believe that I was right. Your reply, however, gave a positive confirmation of my guess. Thanks again - now I have a much better grasp of this concept.

Yang