Magnitude of Complex Exponential Polynomial Inequality

[eric.williams]

Homework Statement

Digital filter analysis - this is just one part of a multi-part question I can't move forward with. It's supposed to be an auxilliary question and isn't the "meat" of the problem.

Find b, such that maximum of the magnitude of the frequency response function b/(1-0.8e\^{-jw}+0.81e^{-j2w}) is 1

Homework Equations

The Attempt at a Solution

I've tried decomposing real and imaginary sinusoids but I'm unsure how to use them in the absolute value function. I never had an intuitive understanding of this in undergrad, and now at the graduate level it's simply expected to be second nature.

 

[lanedance]

first find the w that maximises the expression, then take the magnitude and b will b equal to 1 divded by that result