Working directly from definition, prove that if zn and w, are se- quences of complex numbers with lim zn = 4+ 3i, and lim wn = 4 – 3i, then lim z, · w, = 25. (You may use the fact that convergent complex se- n00 quences are bounded.)

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.2: Remainder And Factor Theorems
Problem 53PS
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4.
Working directly from definition, prove that if z, and w, are se-
quences of complex numbers with
lim zn = 4 + 3i,
and
lim wn = 4 – 3i,
then lim z, · Wn = 25. (You may use the fact that convergent complex se-
quences are bounded.)
Transcribed Image Text:4. Working directly from definition, prove that if z, and w, are se- quences of complex numbers with lim zn = 4 + 3i, and lim wn = 4 – 3i, then lim z, · Wn = 25. (You may use the fact that convergent complex se- quences are bounded.)
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