To determine To express: The complex number − 1 − i in the form R ( cos θ + i sin θ ) = Re i θ . Explanation Consider the complex number − 1 − i . It is known that, for a complex number z = a + i b , the modulus R , is given R = | z | = a 2 + b 2 . Argument θ can be obtained from tan θ = b a . By comparing the given complex number − 1 − i with z = a + i b , the values of a = − 1 and b = − 1 . Obtain the value of R as follows. R = | z | = ( − 1 ) 2 + ( − 1 ) 2 = 1 + 1 R = 2 Obtain the value of θ as follows. tan θ = − 1 − 1 = 1 θ = tan − 1 ( 1 ) θ = π 4 Since, a is negative and b is negative, so θ lies in the third quadrant

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ISBN: 9780470458327

Author: William E. Boyce, Richard C. DiPrima

Publisher: Wiley, John & Sons, Incorporated

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Chapter 4.2, Problem 6P

To determine

To express: The complex number −1−i in the form R(cosθ+isinθ)=Reiθ.

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Chapter 4.2, Problem 5P

Chapter 4.2, Problem 7P

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Chapter 4 Solutions

Elementary Differential Equations

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