Math Problem Statement

  1. (i) Find the transformation which maps the triangular region 0 <= arg(z) <= pi/3 into the unit circle |w| <= 1

(ii) Find the image of the grid which consists of the vertical line segments x = 1,2 and 3, (- 3pi)/4 <= y <= (2pi)/3) and the horizontal line segments y = (-3pi)/4,-pi/4,0,pi/2and, 1 <= x <= 3 under w = e^z

Solution

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Math Problem Analysis

Mathematical Concepts

Complex Analysis
Conformal Mapping
Exponential Function

Formulas

Mapping formulas for complex functions

Theorems

Schwarz Lemma

Suitable Grade Level

Advanced Undergraduate

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