Word Count : 477

---

We are asked to find the maximum and minimum of ( |f(z)| ) for ( f(z) = z^2 - z ) over the closed unit disk ( R = { z : |z| \le 1 } ). We solve this step by step manually. --- Let ( z = x + iy ), where ( x, y \in \mathbb{R} ). Then [ f(z) = z^2 - z = (x + iy)^2 - (x + iy) = (x^2 - y^2 ___ __________ ___ ___ _____ _________.
____ _______ ____ ______ _________ ____ ______ ______ __________ ___ _______ ____.
___ _____ _____ _____ ____.
______ _______ _______ _________ ________ _______ ____ ______ _________ _______ __________ ________.
__________ _____ ________ ______ ______ _________ ___ ____.
_________ ____ _______ ________ ____ ______ ____.
_______ ____ ____ ______ ______ _______ ___ _______ ____.
______ _______ _________ ______ ________ ____.
_______ __________ ____ ________ _______ ____ ________ ______ ________ _______ ____.
______ ______ ___ ________ ____ ___ ___.
_______ __________ _______ ___ ____ __________ _____ ________ _________ ______ __________.
__________ _________ ____ ________ ____ _______ ________ ________ ____ ___ ___ __________.
_____ _____ ___ ______ ____ __________ _______.
___ _________ _____ ________ __________ ________.
_____ _________ __________ _____ _______ ____ ________.
___ _________ _____ ________ ____ _________ ________ _________ _______ _______ ______ ___.
________ ______ ____ _______ ________ _______.
__________ ___ _____ _________ __________ _____ _____.
__________ ____ ______ ____ _____ _________ ___ _________ _____ ___ ________.
______ ______ _____ _______ _______ _______ ____ ____.
_______ ________ __________ __________ ________ ____ _____ ____ ______ ____ _________ ________.
_______ _____ ______ _____ ________ _________ __________.
_______ ____ ___ ______ _____ _________ _______ _________.
_________ _______ _______ ___ ______ ____ ________ ______ ___ ________ _______.
_________ _______ ____ ___ _____ _________ ___ ___ ____ ____.
_________ _____ _________ ______ ________ ___ _________ _______ __________ ______ ___.
____ _______ _______ _________ _______.
_______ ______ ___ _________ ________ _____ _______ __________ ____ ______ ________.
__________ ___ ________ _______ ______ ____ ____ ______ _____ ________.
_______ ____ ________ _______ _______ ____ _______ ______ ____ _______.
____ __________ _______ _______ _____ _____.
_________ ________ ___ __________ __________ __________.
_________ ____ ___ _________ _________ ___ ___ _______ ___ _________ ____.
___ ______ _________ _____ _______ _____ ________ ______ _____ _________ _____.
________ ______ ___ ________ ________ ____ _____ _____ ________.
_____ ______ _____ ________ _______ ________ _______ _______.
_______ _____ __________ ______ _________.
________ ___ _______ _____ _________ ___ ________ __________ ____ ________ ______.
_________ ___ _______ ___ _______ ___ ________ __________ _____ ____ _____.
_________ _________ ____ ___ ______ ______ ______ _____ ____.
_________ ____ ___ ______ ________ ____ _______.
_________ _____ ________ _____ ______ _____ ________ ____ __________ ________ ________ _________.
_______ __________ ___ ____ ______.
________ _________ ________ _____ ________.
__________ ___ ______ _______ _______ ___ __________ ______ ___.
_________ ________ _________ _______ _______ ___ _____ ________.
Get Full Answer on WhatsApp