Complex numbers

  • Thread starter Dirac8767
  • Start date
  • #1
11
0
I have the following equation below but i am unsure about the method of finding the variable C. Sorry if its hard to read.

1.41 = |(1+1.10iC)/(1+0.1iC)|

Many thanks
 

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
4,306
48
Maybe multiplying by (1 - 0.1iC)/(1 - 0.1iC) inside the magnitude bars will make your life easier :)
 
  • #3
Mute
Homework Helper
1,388
10
Do you know how the magnitude of a complex number is defined?

If z = x + iy, then the magnitude of z is

[tex]|z| = \sqrt{zz^\ast} = \sqrt{x^2 + y^2}[/tex]

where [itex]z^\ast = x - iy[/itex]. One can show that if z and w are complex numbers, then |z/w| = |z|/|w|. You can use this fact to help solve your problem. (This method won't require CompuChip's hint).
 
  • #4
11
0
Do you know how the magnitude of a complex number is defined?

If z = x + iy, then the magnitude of z is

[tex]|z| = \sqrt{zz^\ast} = \sqrt{x^2 + y^2}[/tex]

where [itex]z^\ast = x - iy[/itex]. One can show that if z and w are complex numbers, then |z/w| = |z|/|w|. You can use this fact to help solve your problem. (This method won't require CompuChip's hint).

Okay, but im still struggling to see how that will help me solve for C
 
  • #5
Mute
Homework Helper
1,388
10
Okay, but im still struggling to see how that will help me solve for C

If I gave you the problem

[tex]A = \sqrt{\frac{a^2 + d^2x^2}{b^2 + c^2x^2}}[/tex]

could you solve for x?

My advice helps you make your expression look like this one. If you can solve this one above, you can solve your problem. Can you see how to get from your original expression to a form looking like the one above using the fact that for complex numbers z and w, |z/w| = |z|/|w| and using the definition of the magnitude of a complex number, [itex]|z| = |x + iy| = \sqrt{x^2 + y^2}[/itex]?
 

Related Threads on Complex numbers

  • Last Post
Replies
2
Views
850
M
  • Last Post
Replies
14
Views
1K
  • Last Post
Replies
4
Views
898
  • Last Post
Replies
12
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
9
Views
1K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
1
Views
2K
Top