To determine To express: The complex number 3 − 4 j in exponential form. Explanation Formula used: The exponential form of the complex number is r e j θ . The rectangular form of the complex number is x + y i . The polar form of the complex number is r ( cos θ + j sin θ ) = r ∠ θ . For any point ( x , y ) in the complex plane, the equations relating x , y , r and θ are, x = r cos θ y = r sin θ r 2 = x 2 + y 2 tan θ = y x Where, the length r is the absolute value and θ is the argument of the complex number. The rectangular form x + y j of a complex number can be converted to the polar form as x + y j = r e j θ by using the above equations. Calculation: It is given that, the rectangular form of the complex number is 3 − 4 j . Compare the complex number 3 − 4 j with the general form of the complex number x + y j . Here, x = 3 and y = − 4 . Obtain the value of r as follows. Substitute x = 3 and y = − 4 in r 2 = x 2 + y 2 . r 2 = ( 3 ) 2 + ( − 4 ) 2 = 9 + 16 r = 25 r = 5 Thus, the value of r is 5

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 12.5, Problem 15E

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To express: The complex number 3−4j in exponential form.

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Chapter 12.5, Problem 14E

Chapter 12.5, Problem 16E

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Chapter 12 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 12.1 - Write in terms of j. Ch. 12.1 - Simplify: 2. Ch. 12.1 - Simplify: 2. Ch. 12.1 - Prob. 4PE Ch. 12.1 - Prob. 5PE Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - In Exercises 1–4, perform the indicated operations...Ch. 12.1 - In Exercises 5–16, express each number in terms of...

Ch. 12.1 - In Exercises 5–16, express each number in terms of...Ch. 12.1 - In Exercises 5–16, express each number in terms of...Ch. 12.1 - Prob. 8E Ch. 12.1 - Prob. 9E Ch. 12.1 - Prob. 10E Ch. 12.1 - Prob. 11E Ch. 12.1 - Prob. 12E Ch. 12.1 - Prob. 13E Ch. 12.1 - Prob. 14E Ch. 12.1 - Prob. 15E Ch. 12.1 - Prob. 16E Ch. 12.1 - In Exercises 17–32, simplify each of the given...Ch. 12.1 - Prob. 18E Ch. 12.1 - Prob. 19E Ch. 12.1 - Prob. 20E Ch. 12.1 - Prob. 21E Ch. 12.1 - Prob. 22E Ch. 12.1 - Prob. 23E Ch. 12.1 - Prob. 24E Ch. 12.1 - In Exercises 17–32, simplify each of the given...Ch. 12.1 - Prob. 26E Ch. 12.1 - Prob. 27E Ch. 12.1 - Prob. 28E Ch. 12.1 - Prob. 29E Ch. 12.1 - Prob. 30E Ch. 12.1 - Prob. 31E Ch. 12.1 - Prob. 32E Ch. 12.1 - Prob. 33E Ch. 12.1 - Prob. 34E Ch. 12.1 - Prob. 35E Ch. 12.1 - Prob. 36E Ch. 12.1 - Prob. 37E Ch. 12.1 - Prob. 38E Ch. 12.1 - Prob. 39E Ch. 12.1 - Prob. 40E Ch. 12.1 - Prob. 41E Ch. 12.1 - Prob. 42E Ch. 12.1 - Prob. 43E Ch. 12.1 - Prob. 44E Ch. 12.1 - Prob. 45E Ch. 12.1 - 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Ch. 12.5 - Prob. 1E Ch. 12.5 - Prob. 2E Ch. 12.5 - In Exercises 3-22, express the given numbers in...Ch. 12.5 - In Exercises 3-22, express the given numbers in...Ch. 12.5 - Prob. 5E Ch. 12.5 - Prob. 6E Ch. 12.5 - Prob. 7E Ch. 12.5 - Prob. 8E Ch. 12.5 - In Exercises 3-22, express the given numbers in...Ch. 12.5 - Prob. 10E Ch. 12.5 - Prob. 11E Ch. 12.5 - Prob. 12E Ch. 12.5 - Prob. 13E Ch. 12.5 - Prob. 14E Ch. 12.5 - In Exercises 3-22, express the given numbers in...Ch. 12.5 - Prob. 16E Ch. 12.5 - Prob. 17E Ch. 12.5 - Prob. 18E Ch. 12.5 - Prob. 19E Ch. 12.5 - Prob. 20E Ch. 12.5 - Prob. 21E Ch. 12.5 - Prob. 22E Ch. 12.5 - Prob. 23E Ch. 12.5 - In Exercises 23–30, express the given complex...Ch. 12.5 - Prob. 25E Ch. 12.5 - Prob. 26E Ch. 12.5 - In Exercises 23–30, express the given complex...Ch. 12.5 - Prob. 28E Ch. 12.5 - Prob. 29E Ch. 12.5 - Prob. 30E Ch. 12.5 - In Exercises 31–34, perform the indicated...Ch. 12.5 - Prob. 32E Ch. 12.5 - Prob. 33E Ch. 12.5 - Prob. 34E Ch. 12.5 - Prob. 35E Ch. 12.5 - 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Prob. 36E Ch. 12.6 - Prob. 37E Ch. 12.6 - In Exercises 35–40, use DeMoivre’s theorem to find...Ch. 12.6 - Prob. 39E Ch. 12.6 - Prob. 40E Ch. 12.6 - Prob. 41E Ch. 12.6 - Prob. 42E Ch. 12.6 - Prob. 43E Ch. 12.6 - Prob. 44E Ch. 12.6 - In Exercises 41–46, find all of the roots of the...Ch. 12.6 - Prob. 46E Ch. 12.6 - Prob. 47E Ch. 12.6 - Prob. 48E Ch. 12.6 - Prob. 49E Ch. 12.6 - Prob. 50E Ch. 12.6 - Prob. 51E Ch. 12.6 - Prob. 52E Ch. 12.6 - The electric power p (in W) supplied to an element...Ch. 12.6 - Prob. 54E Ch. 12.6 - Prob. 55E Ch. 12.6 - Prob. 56E Ch. 12.7 - Prob. 1PE Ch. 12.7 - Prob. 1E Ch. 12.7 - Prob. 2E Ch. 12.7 - Prob. 3E Ch. 12.7 - Prob. 4E Ch. 12.7 - Prob. 5E Ch. 12.7 - Prob. 6E Ch. 12.7 - Prob. 7E Ch. 12.7 - Prob. 8E Ch. 12.7 - Prob. 9E Ch. 12.7 - Prob. 10E Ch. 12.7 - Prob. 11E Ch. 12.7 - Prob. 12E Ch. 12.7 - Prob. 13E Ch. 12.7 - Prob. 14E Ch. 12.7 - Prob. 15E Ch. 12.7 - Prob. 16E Ch. 12.7 - Prob. 17E Ch. 12.7 - Prob. 18E Ch. 12.7 - Prob. 19E Ch. 12.7 - Prob. 20E Ch. 12.7 - Prob. 21E Ch. 12.7 - Prob. 22E Ch. 12.7 - Prob. 23E Ch. 12.7 - Prob. 24E Ch. 12 - Prob. 1RE Ch. 12 - Prob. 2RE Ch. 12 - Prob. 3RE Ch. 12 - Prob. 4RE Ch. 12 - Prob. 5RE Ch. 12 - Prob. 6RE Ch. 12 - Prob. 7RE Ch. 12 - Prob. 8RE Ch. 12 - Prob. 9RE Ch. 12 - Prob. 10RE Ch. 12 - Prob. 11RE Ch. 12 - Prob. 12RE Ch. 12 - Prob. 13RE Ch. 12 - Prob. 14RE Ch. 12 - Prob. 15RE Ch. 12 - Prob. 16RE Ch. 12 - Prob. 17RE Ch. 12 - Prob. 18RE Ch. 12 - Prob. 19RE Ch. 12 - Prob. 20RE Ch. 12 - Prob. 21RE Ch. 12 - Prob. 22RE Ch. 12 - Prob. 23RE Ch. 12 - Prob. 24RE Ch. 12 - Prob. 25RE Ch. 12 - Prob. 26RE Ch. 12 - Prob. 27RE Ch. 12 - Prob. 28RE Ch. 12 - Prob. 29RE Ch. 12 - Prob. 30RE Ch. 12 - Prob. 31RE Ch. 12 - In Exercises 29–36, give the polar and exponential...Ch. 12 - In Exercises 29–36, give the polar and exponential...Ch. 12 - In Exercises 29–36, give the polar and exponential...Ch. 12 - In Exercises 29–36, give the polar and exponential...Ch. 12 - Prob. 36RE Ch. 12 - Prob. 37RE Ch. 12 - In Exercises 37–48, give the rectangular form of...Ch. 12 - In Exercises 37–48, give the rectangular form of...Ch. 12 - In Exercises 37–48, give the rectangular form of...Ch. 12 - In Exercises 37–48, give the rectangular form of...Ch. 12 - Prob. 42RE Ch. 12 - Prob. 43RE Ch. 12 - Prob. 44RE Ch. 12 - In Exercises 37–48, give the rectangular form of...Ch. 12 - Prob. 46RE Ch. 12 - Prob. 47RE Ch. 12 - Prob. 48RE Ch. 12 - Prob. 49RE Ch. 12 - Prob. 50RE Ch. 12 - Prob. 51RE Ch. 12 - Prob. 52RE Ch. 12 - Prob. 53RE Ch. 12 - Prob. 54RE Ch. 12 - Prob. 55RE Ch. 12 - Prob. 56RE Ch. 12 - Prob. 57RE Ch. 12 - Prob. 58RE Ch. 12 - Prob. 59RE Ch. 12 - Prob. 60RE Ch. 12 - Prob. 61RE Ch. 12 - Prob. 62RE Ch. 12 - Prob. 63RE Ch. 12 - Prob. 64RE Ch. 12 - Prob. 65RE Ch. 12 - Prob. 66RE Ch. 12 - Prob. 67RE Ch. 12 - Prob. 68RE Ch. 12 - Prob. 69RE Ch. 12 - Prob. 70RE Ch. 12 - Prob. 71RE Ch. 12 - Prob. 72RE Ch. 12 - Prob. 73RE Ch. 12 - Prob. 74RE Ch. 12 - Prob. 75RE Ch. 12 - Prob. 76RE Ch. 12 - Prob. 77RE Ch. 12 - Prob. 78RE Ch. 12 - Prob. 79RE Ch. 12 - Prob. 80RE Ch. 12 - 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