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: The given number and complex number are 30 + 40 j and 5 − 12 j . Compute the polar form of the complex number 30 + 40 j as follows. Compare the complex number 30 + 40 j with the general form of the complex number x + y j . Here, x = 30 and y = 40 . Obtain the value of r as follows. Substitute x = 30 and y = 40 in r 2 = x 2 + y 2 . r 2 = 30 2 + 40 2 r = 30 2 + 40 2 r = 900 + 1600 r = 2500 r = 50 That is, the value of r is 50. Obtain the angle θ as follows. Substitute x = 30 and y = 40 in tan θ = y x . tan θ = 40 30 θ ref = tan − 1 ( 40 30 ) θ ref = 53.1 ° That is, the angle θ ref is 53 To determine To perform: The indicated operation in the expression 30 + 40 j 5 − 12 j and express the result in rectangular and polar form. To determine To check: The answer by performing the indicated operation on 30 + 40 j 5 − 12 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 31E

To determine

To change: The complex numbers 30+40j and 5−12j into polar form.

To determine

To perform: The indicated operation in the expression 30+40j5−12j and express the result in rectangular and polar form.

To determine

To check: The answer by performing the indicated operation on 30+40j5−12j in rectangular form.

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Chapter 12.6, Problem 30E

Chapter 12.6, Problem 32E

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