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Answer this question in Rectangular and Polar forms

Answer this question in Rectangular and Polar forms

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Answer this question in Rectangular and Polar forms

The expression shown is a mathematical operation involving complex numbers in polar form and rectangular form. Here's a detailed explanation of this expression: ### Expression: \[ (b) \quad \frac{(10 \angle 60^\circ)(35 \angle -50^\circ)}{(2 + j6) - (5 + j)} \] ### Explanation: 1. **Numerator: Polar Form Multiplication** - The numerator consists of two complex numbers in polar form: - \(10 \angle 60^\circ\) - \(35 \angle -50^\circ\) - To multiply two numbers in polar form, multiply their magnitudes and add their angles: \[ \text{Magnitude: } 10 \times 35 = 350 \] \[ \text{Angle: } 60^\circ + (-50^\circ) = 10^\circ \] - Thus, the result of the multiplication is: \[ 350 \angle 10^\circ \] 2. **Denominator: Rectangular Form Subtraction** - The denominator consists of two complex numbers in rectangular form: - \(2 + j6\) - \(5 + j\) - To subtract these numbers, subtract corresponding real and imaginary parts: \[ \text{Real part: } 2 - 5 = -3 \] \[ \text{Imaginary part: } 6 - 1 = 5 \] - Thus, the result of the subtraction is: \[ -3 + j5 \] Overall, the expression involves operating with complex numbers in different forms (polar and rectangular) and demonstrates basic multiplication and subtraction principles in complex arithmetic.
Transcribed Image Text:The expression shown is a mathematical operation involving complex numbers in polar form and rectangular form. Here's a detailed explanation of this expression: ### Expression: \[ (b) \quad \frac{(10 \angle 60^\circ)(35 \angle -50^\circ)}{(2 + j6) - (5 + j)} \] ### Explanation: 1. **Numerator: Polar Form Multiplication** - The numerator consists of two complex numbers in polar form: - \(10 \angle 60^\circ\) - \(35 \angle -50^\circ\) - To multiply two numbers in polar form, multiply their magnitudes and add their angles: \[ \text{Magnitude: } 10 \times 35 = 350 \] \[ \text{Angle: } 60^\circ + (-50^\circ) = 10^\circ \] - Thus, the result of the multiplication is: \[ 350 \angle 10^\circ \] 2. **Denominator: Rectangular Form Subtraction** - The denominator consists of two complex numbers in rectangular form: - \(2 + j6\) - \(5 + j\) - To subtract these numbers, subtract corresponding real and imaginary parts: \[ \text{Real part: } 2 - 5 = -3 \] \[ \text{Imaginary part: } 6 - 1 = 5 \] - Thus, the result of the subtraction is: \[ -3 + j5 \] Overall, the expression involves operating with complex numbers in different forms (polar and rectangular) and demonstrates basic multiplication and subtraction principles in complex arithmetic.
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