1) Are the following functions analytic? a) f (z) = z z b) f(z) = z + z2

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 45E
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1) Are the following functions analytic?
a) f (z) = z z
Z Z
b) f(z) = z + z²
d
1
2) Prove that: (tan-1 z) =
1+z2
dz
3) Find the expention of sin³ 0
4) Proof that: cosh iz = cos z
5) Prove that: cosh? z – sinh? z = 1
-
6) Prove that: cosh? z + sinh? z = cosh 2z
Transcribed Image Text:1) Are the following functions analytic? a) f (z) = z z Z Z b) f(z) = z + z² d 1 2) Prove that: (tan-1 z) = 1+z2 dz 3) Find the expention of sin³ 0 4) Proof that: cosh iz = cos z 5) Prove that: cosh? z – sinh? z = 1 - 6) Prove that: cosh? z + sinh? z = cosh 2z
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