what the difference between the phase of f(z) and |f(z)|

I want to plot the complex function f(z) and I am tring to plot |f(z)| as well , but I can not understand what the difference between them?

I mean what does f(z) represent and what does |f(z)| represent and which of them represent exactly the complex function.

I appreciate any help

[Mathieu NOE]

hello

|f(z)| is the modulus of the complex function f(z) so it will represent only the amplitude (or modulus) of a complex valued function. the phase information is lost

Answer 1

[Anagha Mittal]

Hi!

The difference between f(z) and |f(z)| is that the former has all the actual values of the complex function while the latter only has the positive values (i.e. the positives remain the same and the sign is reversed for negative values).

|f(z)| is the modulus of f(z) which returns only positive values.

For the exact representation, you may plot f(z).

[Walter Roberson]

However for complex functions, the magnitude is sqrt(real^2 + imag^2). For locations where the samples are real, then this corresponds to x if x>=0 and -x for x<0. But when there is an imaginary part, it is not meaningful to talk about comparing all the value to 0

The magnitude of f(x) corresponds to rotating each point in the complex plane over to the positive x axes, preserving vector magnitude. The result has no remaining phase.