(a) Prove that the above definition makes sense, by showing that the series converges for every complex number z. Moreover, show that the conver- gence is uniform5 on every bounded subset of C. (b) If 21, 22 are two complex numbers, prove that e²¹ e²² = e²¹+22. [Hint: Use the binomial theorem to expand (z₁+z2)", as well as the formula for the binomial coefficients.]
(a) Prove that the above definition makes sense, by showing that the series converges for every complex number z. Moreover, show that the conver- gence is uniform5 on every bounded subset of C. (b) If 21, 22 are two complex numbers, prove that e²¹ e²² = e²¹+22. [Hint: Use the binomial theorem to expand (z₁+z2)", as well as the formula for the binomial coefficients.]
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
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