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Let f(z) - 5 | 4, if z ‡ 0, if z = 0 Prove the following: - 1. The function of is continuous at the point z₁ = 0). 2. The Cauchy-Riemann equations are satisfied at Zo = = 0. 3. The function f does not have a complex derivative at zo = 0.

Let f(z) - 5 | 4, if z ‡ 0, if z = 0 Prove the following: - 1. The function of is continuous at the point z₁ = 0). 2. The Cauchy-Riemann equations are satisfied at Zo = = 0. 3. The function f does not have a complex derivative at zo = 0.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.5: Solution Of Cubic And Quartic Equations By Formulas (optional)
Problem 29E
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Let f(z) - 5 | 4, if z ‡ 0, if z = 0 Prove the following: - 1. The function of is continuous at the point z₁ = 0). 2. The Cauchy-Riemann equations are satisfied at Zo = = 0. 3. The function f does not have a complex derivative at zo = 0.
Transcribed Image Text:Let f(z) - 5 | 4, if z ‡ 0, if z = 0 Prove the following: - 1. The function of is continuous at the point z₁ = 0). 2. The Cauchy-Riemann equations are satisfied at Zo = = 0. 3. The function f does not have a complex derivative at zo = 0.
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