Hi everybody,

Question,

Find the argument of z for each of the following in the interval [0,2pie]. (Give exact answers where possible)

z=3+2i

the answer is 0.588

please show the working out aswell. Thanks everyone.

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- August 6th 2009, 01:54 AMAwsom Guy[SOLVED] Complex Numbers
Hi everybody,

Question,

Find the argument of z for each of the following in the interval [0,2pie]. (Give exact answers where possible)

z=3+2i

the answer is 0.588

please show the working out aswell. Thanks everyone. - August 6th 2009, 03:02 AMPlato
- August 6th 2009, 03:13 AMAwsom Guyumm..
- August 6th 2009, 05:28 AMmr fantastic
- August 6th 2009, 06:35 AMAmer
- August 6th 2009, 04:03 PMHallsofIvy
The real question appears to be: Do you know the

**definition**of "argument" of a complex number? - August 7th 2009, 01:05 AMAwsom GuyConfused
- August 7th 2009, 03:49 AMmr fantastic
- August 7th 2009, 09:18 AMAmer
complex numbers written in general as

right

then the argument of z given by

since the argument is values so to find theta values take arctan ( ) for both sides you will have

the argument of z denoted by arg(z)

note:- argument of z have infinitely many values

the principle argument of z denoted by Arg(z) is the unique value of such that as you can see the principle argument take one value

you can say that

n integar number

Examples:-

Find the argument and the principle argument to the following:

y=1 and x=sqrt{3} so

the tan is negative in the second quarter and in the third quarter but the principle argument take the values in the interval

or to make it easier to determine the angle write it

so

to make it easier to determine the angle

I think it is clear now