# Inequalities of negative arguments in complex numbers

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1. Dec 15, 2015

### toforfiltum

1. The problem statement, all variables and given/known data
Arg z≤ -π /4

2. Relevant equations

3. The attempt at a solution
I'm confused whether the answer to that would be more than -45° or less. Should the approach to arguments be the same as in negative numbers?

2. Dec 15, 2015

### SammyS

Staff Emeritus
The problem is the same whether stated in degrees or in radians.

Yes, the approach is the same as for negative numbers.

Regardless of the signs of two numbers, a < b means that b - a is positive.

3. Dec 15, 2015

### toforfiltum

Thanks! To confirm, the answer would be 60°...etc?

4. Dec 15, 2015

### Staff: Mentor

???
60° is a positive angle. Do you know how to convert from radians to degrees? Your answer above suggests that you don't.
The answer would not be a single number. It would be an interval of numbers, all of which are less than $-\pi/4$.

5. Dec 15, 2015

### SammyS

Staff Emeritus
Is it true that 60° ≤ -45° ?

6. Dec 15, 2015

### jk22

Maybe you are confused with the fact that the argument is defined modulo two pi ?

7. Dec 15, 2015

### Ray Vickson

You need to decide whether you are taking $\arg \, z$ in $[0, 2\pi]$ in $[-\pi, \pi]$.

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