Explanation Formula used: Polar form : 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 ( cos θ + j sin θ ) by using the above equations. Calculation: It is given that, the complex number are 7 − 3 j and 8 + j . Compute the polar form of the complex number 7 − 3 j as follows. Compare the complex number 7 − 3 j with the general form of the complex number x + y j . Here, x = 7 and y = − 3 . Obtain the value of r as follows. Substitute x = 7 and y = − 3 in r 2 = x 2 + y 2 . r 2 = 7 2 + ( − 3 ) 2 r = 7 2 + ( − 3 ) 2 r = 49 + 9 r = 7.62 That is, the value of r is 7.62. Obtain the angle θ as follows. Substitute x = 7 and y = − 3 in tan θ = y x . tan θ = − 3 7 θ ref = tan − 1 ( − 3 7 ) θ ref = − 23.19 ° θ ref = − 23 To determine To perform: The indicated operation in the expression ( 7 − 3 j ) ( 8 + j ) ; Express the result in rectangular and polar form. To determine To check: The answer by performing the product on the complex numbers 7 − 3 j and 8 + j in rectangular form.

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780134434636

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Question

Chapter 12.6, Problem 27E

To determine

To change: The complex numbers 7−3j and 8+j into polar form.

To determine

To perform: The indicated operation in the expression (7−3j)(8+j); Express the result in rectangular and polar form.

To determine

To check: The answer by performing the product on the complex numbers 7−3j and 8+j in rectangular form.

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Chapter 12.6, Problem 26E

Chapter 12.6, Problem 28E

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