Explanation Given information: The given functions are, | z + 3 | = 1 − i z z = x + i y Square both side in the given complex expression. | z + 3 | 2 = ( 1 − i z ) 2 ( z + 3 ) ( z + 3 ¯ ) = 1 − z 2 − 2 i z ( z + 3 ) ( z ¯ + 3 ) = 1 − z 2 − 2 i z z z ¯ + 3 ( z + z ¯ ) + 9 = 1 − z 2 − 2 i z ...... (1) The important results are, ⇒ z z ¯ = x 2 + y 2 z + z ¯ = 2 x z 2 = x 2 − y 2 + 2 i x y Use the above result in equation (1). x 2 + y 2 + 3 ( 2 x ) + 9 = 1 − ( x 2 − y 2 + 2 i x y ) − 2 i ( x + i y ) x 2 + y 2 + 6 x + 8

Mathematical Methods in the Physical Sciences

3rd Edition

ISBN: 9780471198260

Author: Mary L. Boas

Publisher: Wiley, John & Sons, Incorporated

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Chapter 2.17, Problem 13MP

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To find: the real x and y for the given expression.

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Chapter 2.17, Problem 12MP

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Chapter 2 Solutions

Mathematical Methods in the Physical Sciences

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the real x and y for the given expression.

Solution Summary: The author explains the solution for z=x+iy, which satisfies the given function.

To find: the real x and y for the given expression.

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Chapter 2 Solutions