(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the maximum value of |(z-1)(z+1/2)| for |z|≤1.

2. Relevant equations

Calculus min/max concepts?

3. The attempt at a solution

Let f(z)=|(z-1)(z+1/2)|. Observe f(z) is the product of 2 analytic functions on |z|≤1, g(z)=z-1 and h(z)=z+1/2. Therefore f(z) is analytic on |z|≤1. Since f(z) is analytic on |z|≤1, it is continuous on the same domain.

f'(z)=2z-1/2.

Critical points at z=1 and 1/4.

f(1)=0

f(1/4)=9/16

The maximum value of |(z-1)(z+1/2)| for |z|≤1 is 9/16.

Is this close? I suspect I'm missing something fundamental as this doesn't use any complex analysis content.

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# Homework Help: Maximum Value Complex Function

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