Math Problem Statement

Where does the function w=z^2 map the range D={z: Imz>0}?

Solution

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Math Problem Analysis

Mathematical Concepts

Complex Analysis
Complex Functions
Transformation of Complex Planes

Formulas

w = z^2
w = (x + iy)^2 = x^2 - y^2 + 2ixy

Theorems

Mapping of the Upper Half-Plane
Transformation of Complex Functions

Suitable Grade Level

Undergraduate Level (College)