# Homework Help: Polar form and arg(z) problem

1. Apr 7, 2012

### charmedbeauty

1. The problem statement, all variables and given/known data

express the arg(z) and polar form of

($1/\sqrt{2}$) - ($i/\sqrt{2}$)

2. Relevant equations

3. The attempt at a solution

Ok so I did $\sqrt{(1/\sqrt{2})^{2}+(1/\sqrt{2})^{2}}$ = 1

so tan$^{-1}$(1) = $\pi/4$ so arg(z)=5$\pi$$/4$

but they had the answer as $-3\pi/4$

Am I wrong or are they because shouldnt the arg(z) lie in the third quad.??

2. Apr 8, 2012

### Office_Shredder

Staff Emeritus
A better question for you is why do those numbers represent the same angle

3. Apr 8, 2012

### HallsofIvy

Both $5\pi/4$ and $-3\pi/4$ are in the third quadrant.

4. Apr 8, 2012

### scurty

Were they asking for the principal argument? i.e. Arg(z)? Arg(z) is defined to be in the range of $(-\pi,\pi]$