Matlab won't find complex magnitude?

I am trying to find the complex magnitude of this transfer function for a low pass filter

syms H w R C f
H = 1/(sqrt(-1)*w*C*R+1)
H = simplify(abs(H))

Creates

How do I get:

I have tried

H = rewrite(H, 'sqrt')

And have gotten literally the same thing. I am starting to think such a simple thing is not possible. The goal is to evaluate this transfer function at the cutoff frequency (-3db)

w = solve(H == sqrt(1/2), w)

But I cannot do this unless I have the complex magnitude. Yes I can do this by hand but I have another script which is supposed to evaluate a large equation and doing it by hand would take ages. Thank you.

Answer 1

[ioannis gregos]

Figured it out. You must set assumptions of the variables, whether they are real or complex. Matlab doesn't know how to interpret your symbolic variables so it doesn't.

use the syms 'set' command like so:

syms w R C f real
syms H
H = 1/(sqrt(-1)*w*C*R+1)
H = simplify(abs(H))

Should work

If you want to get it in the form sqrt(x^2 + (iy)^2) do:

syms w R C f real
syms H
H = 1/(sqrt(-1)*w*C*R+1)
H = rewrite(abs(H), 'sqrt')