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3. Show that sin? z + cos² z = 1, 2 € C, assuming the corre sponding identity for : €R and using the uniqueness principle. 4. Show that if f and g are an alytic on a domain D and f(2)g(2) = 0 for all z e D, then either f or g must be identically zero in D. %3D

3. Show that sin? z + cos² z = 1, 2 € C, assuming the corre sponding identity for : €R and using the uniqueness principle. 4. Show that if f and g are an alytic on a domain D and f(2)g(2) = 0 for all z e D, then either f or g must be identically zero in D. %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. Show that sin? z + cos² z = 1, z € C, assuming the corre sponding identity for z € R and using the uniqueness principle. 4. Show that if f and g are analytic on a domain D and f(2)g(z) = 0 for all z e D, then either f or g must be identically zero in D. 5. Is there any function f, analytic in |z| < 1, su ch that
Transcribed Image Text:3. Show that sin? z + cos² z = 1, z € C, assuming the corre sponding identity for z € R and using the uniqueness principle. 4. Show that if f and g are analytic on a domain D and f(2)g(z) = 0 for all z e D, then either f or g must be identically zero in D. 5. Is there any function f, analytic in |z| < 1, su ch that
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