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Given Z₁ = 10 + 10j, Z₂ = 20445°, find Z1 Z2 and in the Polar forms. OZ1 Z2 = 282.84290, -0.7140° Z O Z₁ Z2 = 282.84445°, -0.71.445° O Z Z=200/90 = 0.540° OZ1 Z2 200245°, 0.5/45°

Given Z₁ = 10 + 10j, Z₂ = 20445°, find Z1 Z2 and in the Polar forms. OZ1 Z2 = 282.84290, -0.7140° Z O Z₁ Z2 = 282.84445°, -0.71.445° O Z Z=200/90 = 0.540° OZ1 Z2 200245°, 0.5/45°

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 38RE
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Like real numbers, basic operations for complex numbers include Addition, Subtraction, Multiplication, and Division. There are Three forms to represent a complex number, i.e., Polar form (AZO), Exponential form (A. e), and Rectangular form (a+bj). Complex number addition/subtraction in the Rectangular form: Given Z₁ = a+bj, Z₂ = c + d. j. Z+Za+c+ (b+d).j Z1 Z2a c+ (b-d).j Complex number multiplication/division in the Rectangular form: Given Z₁ =a+b.j, Z₂ =c+dj. ZZ (a+bj) (c+dj) = (ac - bd) + (ad + bc) j Z₁ a+bj (a+b)-(c-dj) (ac+bd)+(bc-ad); c+dj (c+dj) (c-dj) cid ac+bd bc-ad + d c² d² J Complex number multiplication/division in the Polar form: Given Z₁ = AZ, Z = BZ0, Z1 Z2 A BZ (+0) Z₁ 2 = 솜<(0-0) Z Let us do some practices. Given Z₁ = 10 + 10j, Z₂ = 20445°, find Z₁ - Z2 and in the Polar forms. OZ-Z2=282.84490°, = 0.7120° O Z1 Z2 = 282.84445°, = 0.71445° OZ1 Z2=200/90 = 0.540° OZ-Z2=200/45°-0.5/45°
Transcribed Image Text:Like real numbers, basic operations for complex numbers include Addition, Subtraction, Multiplication, and Division. There are Three forms to represent a complex number, i.e., Polar form (AZO), Exponential form (A. e), and Rectangular form (a+bj). Complex number addition/subtraction in the Rectangular form: Given Z₁ = a+bj, Z₂ = c + d. j. Z+Za+c+ (b+d).j Z1 Z2a c+ (b-d).j Complex number multiplication/division in the Rectangular form: Given Z₁ =a+b.j, Z₂ =c+dj. ZZ (a+bj) (c+dj) = (ac - bd) + (ad + bc) j Z₁ a+bj (a+b)-(c-dj) (ac+bd)+(bc-ad); c+dj (c+dj) (c-dj) cid ac+bd bc-ad + d c² d² J Complex number multiplication/division in the Polar form: Given Z₁ = AZ, Z = BZ0, Z1 Z2 A BZ (+0) Z₁ 2 = 솜<(0-0) Z Let us do some practices. Given Z₁ = 10 + 10j, Z₂ = 20445°, find Z₁ - Z2 and in the Polar forms. OZ-Z2=282.84490°, = 0.7120° O Z1 Z2 = 282.84445°, = 0.71445° OZ1 Z2=200/90 = 0.540° OZ-Z2=200/45°-0.5/45°
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