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I am very new to Mathematica and I've been trying to use it to perform calculations with complex numbers. I am mainly trying to find the norm of complex expressions with an unknown variable. For example, I am trying to find the norm of 1 over 1 plus ri using Mathematica (where r is the variable and i is the imaginary number i). I have tried looking online and nothing seems to work. For such a simple expression, I can easily compute it by hand, but it becomes a pain to do for bigger expressions. For this specific case, I would be expecting the answer to be 1 over the square root of 1 plus r squared. How do I do this?

Thanks in advance!

[Edit] Sorry for the in-text math stuff, Stack Exchange is preventing me from posting when I am adding math formulas in latex saying that I'm not formatting the code properly.

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I am trying to find the norm of 1 over 1 plus ri using Mathematica (where r is the variable and i is the imaginary number i). I would be expecting the answer to be 1 over the square root of 1 plus r squared

One way is

ClearAll[r]
expr = 1/(1 + r I);
ComplexExpand@Norm@expr

Mathematica graphics

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