Problem 5.6. Let ze C. (a) Prove that |1*| is single-valued if and only if Im z = 0. (b) Find a necessary and sufficient condition for |#| to be single-valued. (c) (extra credit) Show by counterexample that the statement is false: 1* is single-valued if and only if Imz = 0.
Problem 5.6. Let ze C. (a) Prove that |1*| is single-valued if and only if Im z = 0. (b) Find a necessary and sufficient condition for |#| to be single-valued. (c) (extra credit) Show by counterexample that the statement is false: 1* is single-valued if and only if Imz = 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Problem 5.6. Let z € C.
(a) Prove that |1*| is single-valued if and only if Im z = 0.
(b) Find a necessary and sufficient condition for |i#| to be single-valued.
(c) (extra credit) Show by counterexample that the statement is false:
1* is single-valued if and only if Im z = 0.
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