Polar Form of Complex Numbers: Understanding Quadrants and Sign Conventions

[Darth Frodo]

Not homework as such, just need some clarification.

When finding $\alpha$ do you have to take the signs into account when finding tan$^{-1}$ x/a. Does it matter if a or x are negative?

Next question is about quadrants

1: $\theta$ = $\alpha$

2: $\theta$ = $\pi$ - $\alpha$

3: $\theta$ = -$\pi$ - $\alpha$

4: $\theta$ = -$\alpha$

Based on these (if correct) it seems that I should disregard the sign when finding $\alpha$.

Is this correct?

 

[Saitama]

Not homework as such, just need some clarification.

When finding $\alpha$ do you have to take the signs into account when finding tan$^{-1}$ x/a. Does it matter if a or x are negative?

Next question is about quadrants

1: $\theta$ = $\alpha$

2: $\theta$ = $\pi$ - $\alpha$

3: $\theta$ = -$\pi$ - $\alpha$

4: $\theta$ = -$\alpha$

Based on these (if correct) it seems that I should disregard the sign when finding $\alpha$.

Is this correct?

No, signs aren't taken into account while finding $\alpha$.

I am not sure about the 3 quadrant.