• Support PF! Buy your school textbooks, materials and every day products Here!

Inequalities of negative arguments in complex numbers

  • #1
341
4

Homework Statement


Arg z≤ -π /4

Homework Equations




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?
 

Answers and Replies

  • #2
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,219
945

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.
 
  • #3
341
4
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?
 
  • #4
33,070
4,771
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##.
 
  • #5
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,219
945
Thanks! To confirm, the answer would be 60°...etc?
Is it true that 60° ≤ -45° ?
 
  • #6
601
19
Maybe you are confused with the fact that the argument is defined modulo two pi ?
 
  • #7
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,705
1,722

Homework Statement


Arg z≤ -π /4

Homework Equations




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]##.
 

Related Threads for: Inequalities of negative arguments in complex numbers

  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
4
Views
745
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
9
Views
5K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
7K
Top