Explanation The complex number ( 1 − i ) 1 2 is written as: ( 1 − i ) 1 2 = 1 2 + 1 2 e ( − π 4 + m π ) i = 2 e ( − π 4 + m π ) i For m = 0 , the root of the complex number is calculated as: z = [ 2 e [ ( − π 4 + 0 × π ) i ] ] 1 2 = 2 1 4 e ( − π 8 ) i = 2 1 4 [ 1 + cos ( π 4 ) 2 − i 1 − cos ( π 4 ) 2 ] On the further simplification, the following is obtained. z 1 = 2 1 4 [ 2 + 2 2 − i 2 − 2 2 ] = 1

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Author: William E. Boyce, Richard C. DiPrima

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Chapter 4.2, Problem 8P

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The indicated roots of the given complex number (1−i)12.

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Chapter 4 Solutions

Elementary Differential Equations

Ch. 4.1 - In each of Problems 1 through 6, determine...Ch. 4.1 - In each of Problems 1 through 6, determine...Ch. 4.1 - In each of Problems 1 through 6, determine...Ch. 4.1 - In each of Problems 1 through 6, determine...Ch. 4.1 - In each of Problems 1 through 6, determine...Ch. 4.1 - Prob. 6P Ch. 4.1 - In each of Problems 7 through 10, determine...Ch. 4.1 - Prob. 8P Ch. 4.1 - In each of Problems 7 through 10, determine...Ch. 4.1 - Prob. 10P

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The indicated roots of the given complex number ( 1 − i ) 1 2 .

The indicated roots of the given complex number (1−i)12.

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Chapter 4 Solutions