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1. If (x and jy) = 3 + j8, find x and y. x = 2.40 and y = 1.67

1. If (x and jy) = 3 + j8, find x and y. x = 2.40 and y = 1.67

Advanced Engineering Mathematics
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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Express all in polar form.... thank you
12:57 AM O 97% + ADVANCED-MATH-TA... Square Root of Complex Numbers Vz = V+360°k where :k =0 and 1. Polar Form nth Root of Complex Numbers where: Vz = is designated as W, k = 0, 1, 2...(n– 1) W, = principal value or root, and e must be a positive angle. W,, W,..W = auxiliary values or roots De Moivre's Theorem (Abraham de Moivre) Raise both sides to the power of n z" = (rZ0)" z" = r"Zne Exercises 2 1. If (x and jy) = 3 + j8, find x and y. x = 2.40 and y = 1.67 2.24/26.57°, 2.24/206.57° or -2.24/26.570 2. Evaluate the square root of 3 + j4 by two methods. 3. Square root of the product of (3 + j4) and (2 + j8) 4. Square root of the sum of 2 cjs 30°, (6-j3) and 3/25° 6.42264.55° 3.24-2.01° 5. Find the three roots of 8. 220°, 24120°, 2/240° 6. Determine the principal value of (3+ j2)ª-12) 7. Find the quadratic equation whose roots are (3 – j5) and (2 + j4). 14.48/248.03° x2 – 5.099L-11.32° x + 26.07 8. Evaluate (5e" 2") by De Moivre's Theorem and express the result in rectangular form. - 19.15 + j16.07
Transcribed Image Text:12:57 AM O 97% + ADVANCED-MATH-TA... Square Root of Complex Numbers Vz = V+360°k where :k =0 and 1. Polar Form nth Root of Complex Numbers where: Vz = is designated as W, k = 0, 1, 2...(n– 1) W, = principal value or root, and e must be a positive angle. W,, W,..W = auxiliary values or roots De Moivre's Theorem (Abraham de Moivre) Raise both sides to the power of n z" = (rZ0)" z" = r"Zne Exercises 2 1. If (x and jy) = 3 + j8, find x and y. x = 2.40 and y = 1.67 2.24/26.57°, 2.24/206.57° or -2.24/26.570 2. Evaluate the square root of 3 + j4 by two methods. 3. Square root of the product of (3 + j4) and (2 + j8) 4. Square root of the sum of 2 cjs 30°, (6-j3) and 3/25° 6.42264.55° 3.24-2.01° 5. Find the three roots of 8. 220°, 24120°, 2/240° 6. Determine the principal value of (3+ j2)ª-12) 7. Find the quadratic equation whose roots are (3 – j5) and (2 + j4). 14.48/248.03° x2 – 5.099L-11.32° x + 26.07 8. Evaluate (5e" 2") by De Moivre's Theorem and express the result in rectangular form. - 19.15 + j16.07
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