3. Using mathematical induction, prove that the Binomial formula holds for complex numbers (Z1 + Z2)" = k=0 (ziz-k where (1) k whenever Z₁, Z2 € C. Hint: = n! k!(n-k)! ( ₁²₁₁ ) + ( )= ("+¹). - for k= 0, 1,2,....

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 9E
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3. Using mathematical induction, prove that the Binomial formula holds
for complex numbers
11
(2₁ +22)" = Ĺ (1) ²₁22-
k=0
whenever Z₁, Z2 € C.
Hint:
kn-k where
=
n!
k!(n - k)!
n
(₂²₁) + ( )= (" + ¹).
k
for k= 0, 1, 2,....
Transcribed Image Text:3. Using mathematical induction, prove that the Binomial formula holds for complex numbers 11 (2₁ +22)" = Ĺ (1) ²₁22- k=0 whenever Z₁, Z2 € C. Hint: kn-k where = n! k!(n - k)! n (₂²₁) + ( )= (" + ¹). k for k= 0, 1, 2,....
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