# Complex Analysis - The Maximum Modulus Principle

## Homework Statement

Find the maximum of $\left|f\right|$ on the disc of radius 1 in the Complex Plane, for f(z)=3-$\left|z\right|^{2}$

## Homework Equations

The maximum modulus principle?

## The Attempt at a Solution

Since |z| is a real number, then surely the maximum must be 3 when z=0? However, I was reading that the maximum must occur on the boundary, which is |z|=1, for the disc which is described by |z|≤1. What am I doing wrong? Thanks in advance for any help!

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