(1) Given two complex numbers ₁ = r₁(cos 0₁ + i sin 0₁) and Z₂ = r₂(cos 0₂ + i sin 0₂), prove the following formula for the division of complex numbers. [cos(0₁-0₂) + i sin(0₁-0₂)] Z1 Z2 = r₁ 72
(1) Given two complex numbers ₁ = r₁(cos 0₁ + i sin 0₁) and Z₂ = r₂(cos 0₂ + i sin 0₂), prove the following formula for the division of complex numbers. [cos(0₁-0₂) + i sin(0₁-0₂)] Z1 Z2 = r₁ 72
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter7: Real And Complex Numbers
Section7.3: De Moivre’s Theorem And Roots Of Complex Numbers
Problem 8E
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![(1) Given two complex numbers z₁ = r₁(cos 0₁ + i sin 0₁) and Z₂ = r₂(cos 0₂ +
i sin 0₂2), prove the following formula for the division of complex numbers.
Z1
Z2
=
1₁
- [cos(0₁ - 0₂) + i sin(0₁ - 0₂)]
12](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F82aefee1-a4fd-40e7-8b3f-97f92bfc6e2a%2Fa3f8afe1-a40e-4cb2-b8c5-3793ca6f9bd1%2Ft5kapio_processed.png&w=3840&q=75)
Transcribed Image Text:(1) Given two complex numbers z₁ = r₁(cos 0₁ + i sin 0₁) and Z₂ = r₂(cos 0₂ +
i sin 0₂2), prove the following formula for the division of complex numbers.
Z1
Z2
=
1₁
- [cos(0₁ - 0₂) + i sin(0₁ - 0₂)]
12
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