Why Does Arg(z) of a Complex Number Differ in Solutions?

[charmedbeauty]

Homework Statement

express the arg(z) and polar form of

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

Homework Equations

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 shouldn't the arg(z) lie in the third quad.??

 

[Office_Shredder]

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

 

[HallsofIvy]

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

 

[scurty]

Homework Statement

express the arg(z) and polar form of

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

Homework Equations

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 shouldn't the arg(z) lie in the third quad.??

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