1. True-False. If the assertation is true, quote relevant theorem or reason, or give a proof; If false, give a counterexample or other justification. (c) Let G be a region in the complex plane and y a closed smooth path in G. If f is analytic in G, then S,S(2) dz = 0. (d) Let z e C. Then ezt = 1 if and only if z is a real number.
1. True-False. If the assertation is true, quote relevant theorem or reason, or give a proof; If false, give a counterexample or other justification. (c) Let G be a region in the complex plane and y a closed smooth path in G. If f is analytic in G, then S,S(2) dz = 0. (d) Let z e C. Then ezt = 1 if and only if z is a real number.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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I need help with following HW question for complex analysis please 1c & d
![1. True-False. If the assertion is true, quote relevant theorem or reason, or give a proof; If false, give a counterexample or other justification.
(c) Let \( G \) be a region in the complex plane and \( \gamma \) a closed smooth path in \( G \). If \( f \) is analytic in \( G \), then
\[
\int_{\gamma} f(z) \, dz = 0.
\]
(d) Let \( z \in \mathbb{C} \). Then \( \left| e^{zi} \right| = 1 \) if and only if \( z \) is a real number.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0548f28d-2867-4ce8-91e2-809a65372be3%2F3bc8eb3b-4d5c-47bd-84f5-a66ed1b064fa%2Fm2ceso_processed.png&w=3840&q=75)
Transcribed Image Text:1. True-False. If the assertion is true, quote relevant theorem or reason, or give a proof; If false, give a counterexample or other justification.
(c) Let \( G \) be a region in the complex plane and \( \gamma \) a closed smooth path in \( G \). If \( f \) is analytic in \( G \), then
\[
\int_{\gamma} f(z) \, dz = 0.
\]
(d) Let \( z \in \mathbb{C} \). Then \( \left| e^{zi} \right| = 1 \) if and only if \( z \) is a real number.
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