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1.2. Perform arithmetic operations using the polar and exponential form of complex numbers. Complex numbers can be represented in both polar and exponential forms, which offer unique advantages for various mathematical operations. Let Z1 and Z2 be two complex numbers represented in polar form as Z₁ = √₁eiе₁ and Z₂ = 12e102. Perform the following arithmetic operations: i) ii) iii) iv) Calculate Z₁ + Z2 in polar form and express the result as Z3 = re¹03 and in exponential form. Calculate Z1 - Z2 in polar form and express the result as Z4 = √₁e¹04 and in exponential form. Calculate Z1. Z2 in polar form and express the result as Z5 = r5e" form. Calculate Z1 Z2 in polar form and express the result as Z6 = re form. 105 and in exponential 106 and in exponential v) Reflect on the advantages of using polar and exponential forms for complex number operations and how they simplify certain calculations.

1.2. Perform arithmetic operations using the polar and exponential form of complex numbers. Complex numbers can be represented in both polar and exponential forms, which offer unique advantages for various mathematical operations. Let Z1 and Z2 be two complex numbers represented in polar form as Z₁ = √₁eiе₁ and Z₂ = 12e102. Perform the following arithmetic operations: i) ii) iii) iv) Calculate Z₁ + Z2 in polar form and express the result as Z3 = re¹03 and in exponential form. Calculate Z1 - Z2 in polar form and express the result as Z4 = √₁e¹04 and in exponential form. Calculate Z1. Z2 in polar form and express the result as Z5 = r5e" form. Calculate Z1 Z2 in polar form and express the result as Z6 = re form. 105 and in exponential 106 and in exponential v) Reflect on the advantages of using polar and exponential forms for complex number operations and how they simplify certain calculations.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1.2. Perform arithmetic operations using the polar and exponential form of complex numbers. Complex numbers can be represented in both polar and exponential forms, which offer unique advantages for various mathematical operations. Let Z1 and Z2 be two complex numbers represented in polar form as Z₁ = √₁eiе₁ and Z₂ = 12e102. Perform the following arithmetic operations: i) ii) iii) iv) Calculate Z₁ + Z2 in polar form and express the result as Z3 = re¹03 and in exponential form. Calculate Z1 - Z2 in polar form and express the result as Z4 = √₁e¹04 and in exponential form. Calculate Z1. Z2 in polar form and express the result as Z5 = r5e" form. Calculate Z1 Z2 in polar form and express the result as Z6 = re form. 105 and in exponential 106 and in exponential v) Reflect on the advantages of using polar and exponential forms for complex number operations and how they simplify certain calculations.
Transcribed Image Text:1.2. Perform arithmetic operations using the polar and exponential form of complex numbers. Complex numbers can be represented in both polar and exponential forms, which offer unique advantages for various mathematical operations. Let Z1 and Z2 be two complex numbers represented in polar form as Z₁ = √₁eiе₁ and Z₂ = 12e102. Perform the following arithmetic operations: i) ii) iii) iv) Calculate Z₁ + Z2 in polar form and express the result as Z3 = re¹03 and in exponential form. Calculate Z1 - Z2 in polar form and express the result as Z4 = √₁e¹04 and in exponential form. Calculate Z1. Z2 in polar form and express the result as Z5 = r5e" form. Calculate Z1 Z2 in polar form and express the result as Z6 = re form. 105 and in exponential 106 and in exponential v) Reflect on the advantages of using polar and exponential forms for complex number operations and how they simplify certain calculations.
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