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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

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
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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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