# Inequalities of negative arguments in complex numbers

Arg z≤ -π /4

## 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?

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SammyS
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## Homework Statement

Arg z≤ -π /4
2. Homework 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?
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.

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

Mark44
Mentor
Thanks! To confirm, the answer would be 60°...etc?
???
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 $-\pi/4$.

SammyS
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Thanks! To confirm, the answer would be 60°...etc?
Is it true that 60° ≤ -45° ?

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

Ray Vickson
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Arg z≤ -π /4

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