Solving for C in 1.41 = |(1+1.10iC)/(1+0.1iC)|

[Dirac8767]

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

 

[CompuChip]

Maybe multiplying by (1 - 0.1iC)/(1 - 0.1iC) inside the magnitude bars will make your life easier :)

 

[Mute]

Do you know how the magnitude of a complex number is defined?

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

|z| = \sqrt{zz^\ast} = \sqrt{x^2 + y^2}

where z^\ast = x - iy. 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).

 

[Dirac8767]

Do you know how the magnitude of a complex number is defined?

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

|z| = \sqrt{zz^\ast} = \sqrt{x^2 + y^2}

where z^\ast = x - iy. 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 I am still struggling to see how that will help me solve for C

 

[Mute]

Okay, but I am still struggling to see how that will help me solve for C

If I gave you the problem

A = \sqrt{\frac{a^2 + d^2x^2}{b^2 + c^2x^2}}

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, |z| = |x + iy| = \sqrt{x^2 + y^2}?