Explanation Definition used: The complex conjugate of a + i b is a − i b . Calculation: It is given that z 1 = r 1 e i θ 1 and z 2 = r 2 e i θ 2 . Obtain the value of z 1 z 2 as follows. z 1 z 2 = r 1 e i θ 1 r 2 e i θ 2 = r 1 r 2 e i ( θ 1 − θ 2 ) = r 1 r 2 ( cos ( θ 1 − θ 2 ) + i sin ( θ 1 − θ 2 ) ) The complex conjugate of z 1 z 2 = r 1 r 2 ( cos ( θ 1 − θ 2 ) + i sin ( θ 1 − θ 2 ) ) is z 1 z 2 ¯ = r 1 r 2 ( cos ( θ 1 − θ 2 ) − i sin ( θ 1 − θ 2 ) ) . | z 1 z 2 | = z 1 z 2 z 1 z 2 ¯ = { r 1 r 2 ( cos ( θ 1 − θ 2 ) + i sin ( θ 1 − θ 2 ) ) } { r 1 r 2 ( cos ( θ 1 − θ 2 ) − i sin ( θ 1 − θ 2 ) ) } = ( r 1 r 2 <

Calculus, Single Variable: Early Transcendentals (3rd Edition)

3rd Edition

ISBN: 9780134766850

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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Question

Chapter C, Problem 61E

To determine

To prove: The identities |z1z2|=r1r2 and argz1z2=argz1−argz2.

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Chapter C, Problem 60E

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Chapter C Solutions

Calculus, Single Variable: Early Transcendentals (3rd Edition)

Ch. C - Practice Exercises Complex operations Let z = 2 +...Ch. C - Prob. 2E Ch. C - Prob. 3E Ch. C - Prob. 4E Ch. C - Prob. 5E Ch. C - Prob. 6E Ch. C - Prob. 7E Ch. C - Prob. 8E Ch. C - Prob. 9E Ch. C - Prob. 10E

Ch. C - Prob. 11E Ch. C - Prob. 12E Ch. C - Prob. 13E Ch. C - Prob. 14E Ch. C - Prob. 15E Ch. C - Prob. 16E Ch. C - Prob. 17E Ch. C - Prob. 18E Ch. C - Prob. 19E Ch. C - Prob. 20E Ch. C - Prob. 21E Ch. C - Prob. 22E Ch. C - Prob. 23E Ch. C - Prob. 24E Ch. C - Prob. 25E Ch. C - Prob. 26E Ch. C - Prob. 27E Ch. C - Prob. 28E Ch. C - Prob. 29E Ch. C - Prob. 30E Ch. C - Prob. 31E Ch. C - Prob. 32E Ch. C - Prob. 33E Ch. C - Prob. 34E Ch. C - Prob. 35E Ch. C - Prob. 36E Ch. C - Prob. 37E Ch. C - Prob. 38E Ch. C - Prob. 39E Ch. C - Prob. 40E Ch. C - Prob. 41E Ch. C - Prob. 42E Ch. C - Prob. 43E Ch. C - Prob. 44E Ch. C - Prob. 45E Ch. C - Prob. 46E Ch. C - Prob. 47E Ch. C - Prob. 48E Ch. C - Prob. 49E Ch. C - Prob. 50E Ch. C - Prob. 51E Ch. C - Prob. 52E Ch. C - Prob. 53E Ch. C - Prob. 54E Ch. C - Prob. 55E Ch. C - Prob. 56E Ch. C - Prob. 57E Ch. C - Prob. 58E Ch. C - Prob. 59E Ch. C - Prob. 60E Ch. C - Prob. 61E

Knowledge Booster

To prove: The identities | z 1 z 2 | = r 1 r 2 and arg z 1 z 2 = arg z 1 − arg z 2 .

Solution Summary: The author explains the complex conjugate of a+ib, and the value of the result.

To prove: The identities |z1z2|=r1r2 and argz1z2=argz1−argz2.

Want to see the full answer?

Chapter C Solutions