9. Prove the rule for finding the quotient of two complex numbers in polar form. Begin the proof as foll using the conjugate of the denominator's second factor r₁(cos0₁+i sin0₁) r2(cos02-i sin0₂) r₂(cos0₂+isin0₂) r₂(cos0₂-i sin0₂) Perform the indicated multiplications. Then use the difference formulas for sine and cosine. = r₁(cos0₁+i sin0₁) r₂(cos0₂+i sin0₂) .
9. Prove the rule for finding the quotient of two complex numbers in polar form. Begin the proof as foll using the conjugate of the denominator's second factor r₁(cos0₁+i sin0₁) r2(cos02-i sin0₂) r₂(cos0₂+isin0₂) r₂(cos0₂-i sin0₂) Perform the indicated multiplications. Then use the difference formulas for sine and cosine. = r₁(cos0₁+i sin0₁) r₂(cos0₂+i sin0₂) .
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:9. Prove the rule for finding the quotient of two complex numbers in polar form. Begin the proof as follows,
using the conjugate of the denominator's second factor
r₁(cos0₁+i sin0₁)
r₂(cos0₂+i sin0₂)
r₁(cos0₁+i sin0₁)
r2(cos02-i sin0₂)
r₂(cos0₂+i sin0₂)
r₂(cos0₂-i sin0₂)
Perform the indicated multiplications. Then use the difference formulas for sine and cosine.
=
.
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