Chapter 2: Q11P (page 52)

Question:First simplify each of the following numbers to the x+iyform or to the $r e^{i θ}$ form. Then plot the number in the complex plane.
17-12i.

Short Answer

Expert verified

The complex number becomes $z = 20.8 e^{- e 0.615 i}$ .

The graph is mentioned below as:

Step by step solution

Given Information

Thecomplex number is 17 - 12i.

Definition of the Complex number

A complex number is a number that consists of real and imaginary numbers and is written in the form as:

$z = a + i b$ where a and b are real, and z is the complex number.

Find the values

The complex number is 17 - 12i .

Find x and y:

x = 17

y = -12

Find the value of r.

$r = \sqrt{x^{2} + y^{2}} r = \sqrt{{(17)}^{2} + {(- 12)}^{2}} = 20.8$

Find the value of $θ$ :

$θ = \cos^{- 1} (\frac{x}{r}) θ = \cos^{- 1} (\frac{17}{20.8}) = - 35.18 ° = - . 0615 rad z = 20.8 e^{- . 0615 i}$

The complex number becomes $z = 20.8 e^{- . 0615 i}$ .

The graph is mentioned below:

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Question:First simplify each of the following numbers to the x+iyform or to the $r e^{i θ}$ form. Then plot the number in the complex plane.
17-12i.

Short Answer

Step by step solution

Given Information

Definition of the Complex number

Find the values

One App. One Place for Learning.

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Question:First simplify each of the following numbers to the x+iyform or to thereiθform. Then plot the number in the complex plane.17-12i.

Short Answer

Step by step solution

Given Information

Definition of the Complex number

Find the values

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Mechanics and Materials

Translational Dynamics

Fields in Physics

Magnetism and Electromagnetic Induction

Radiation

Nuclear Physics

Study anywhere. Anytime. Across all devices.

Question:First simplify each of the following numbers to the x+iyform or to the $r e^{i θ}$ form. Then plot the number in the complex plane.
17-12i.