Question

2.29. Prove that, If $G \subset C$ is a region and $f: G \to C$ is a complex-valued function with $f''(z)$ defined and equal to 0 for all $z \in G$, then $f(z) = az + b$ for some $a, b \in C$. (Hint: Use Theorem 2.17 to show that $f'(z) = a$, and then use Theorem 2.17 again for the function $f(z) - az$.)

Name: 2.29. Prove that, If G ⊂ C is a region and f: G → C is a complex-valued function with f”(z) defined and equal to 0 for all z ∈ G, then f(z) = az + b for some a, b ∈ C. (Hint: Use Theorem 2.17 to show that f'(z) = a, and then use Theorem 2.17 again for the function f(z) - az.)
Uploaded: 2022-02-22T02:48:26-08:00
Duration: 6 min 8 s
Channel: Tuli H
Description: 2.29. Prove that, If G ⊂ C is a region and f: G → C is a complex-valued function with f”(z) defined and equal to 0 for all z ∈ G, then f(z) = az + b for some a, b ∈ C. (Hint: Use Theorem 2.17 to show that f'(z) = a, and then use Theorem 2.17 again for the function f(z) - az.)

          2.29. Prove that, If $G \subset C$ is a region and $f: G \to C$ is a complex-valued function with $f''(z)$ defined and equal to 0 for all $z \in G$, then $f(z) = az + b$ for some $a, b \in C$. (Hint: Use Theorem 2.17 to show that $f'(z) = a$, and then use Theorem 2.17 again for the function $f(z) - az$.)

2.29. Prove that, If G ⊂ C is a region and f: G → C is a complex-valued function with f”(z) defined and equal to 0 for all z ∈ G, then f(z) = az + b for some a, b ∈ C. (Hint: Use Theorem 2.17 to show that f'(z) = a, and then use Theorem 2.17 again for the function f(z) - az.)

Added by Luis W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Tuli H

02/22/2022

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Step 1: We are given that G CC is a region and f G-C is a complex-valued function with fz defined and equal to 0 for all z E G. Show more…

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2.29.Prove that,If G CC is a region and f G-C is a complex-valued function with fz defined and equal to 0 for all z E G,then f(z)=az+b for some a,b E C.(Hint: Use Theorem 2.17 to show that fz=,and then use Theorem2.17 again for the function fz-az.