Chapter 2: Q12P (page 46)

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.
$3 (c o s 28 ° + i s i n 28 °)$ .

Short Answer

Expert verified

The complex number can be written as $z = 3 e^{0.49 i}$ .

The graph is mentioned below:

Step by step solution

Given Information

The complex number is $3 (c o s 28 ° + i s i n 28 °)$ .

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 $3 (c o s 28 ° + i s i n 28 °)$ .

$z = θ (c o s θ + s i n θ) r = 3 θ = 28 °$

The formulas for x and y are given below.

$x = r \cos (θ) y = r \sin (θ)$

Find x and y:

$x = 3 \cos (28 °) = 2.64 y = 3 \sin (28 °) = 1.41 z = 3 e^{0.49 i}$

The complex number can be written as $z = 3 e^{0.49 i}$ .

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.
$3 (c o s 28 ° + i s i n 28 °)$ .

Short Answer

Step by step solution

Given Information

Definition of the Complex number.

Find the values

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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.3(cos28°+isin28°).

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

Electrostatics

Scientific Method Physics

Dynamics

Electromagnetism

Modern Physics

Classical Mechanics

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.
$3 (c o s 28 ° + i s i n 28 °)$ .