Chapter 2: Q45P (page 54)

Solve for all possible values of the real numbersand in the following equations ${(x + i y)}^{2} = {(x - i y)}^{2}$ .

Short Answer

Expert verified

When x is 0 , y is a real number, and when y is 0 ,x is any real number.

Step by step solution

Given information

It is given that ${(x + i y)}^{2} = {(x - i y)}^{2}$

Definition of a complex number

Every complex number can be described as:

z=a+bi

Whereaandbare both real numbers, z is the complex number, and i is known as iota, which makes z a complex number.

Begin by stating the given information

Evaluate the left- and right-hand sides of the equation:

${(x + i y)}^{2} = x^{2} + 2 x y i - y^{2} {(x - i y)}^{2} = x^{2} - 2 x y i - y^{2}$

The equation can be written as:

$x^{2} + 2 x y i - y^{2} = x^{2} - 2 x y i - y^{2} 2 x y i + 2 x y i = 0$

Equate like terms

Equate like terms from both sides:

$4 x y i = 0 4 x y = 0$

Thus, when x is 0, y is a real number, and when y is 0, x is any real number.

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Solve for all possible values of the real numbersand in the following equations ${(x + i y)}^{2} = {(x - i y)}^{2}$ .

Short Answer

Step by step solution

Given information

Definition of a complex number

Begin by stating the given information

Equate like terms

One App. One Place for Learning.

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Solve for all possible values of the real numbersand in the following equations (x+iy)2=(x-iy)2.

Short Answer

Step by step solution

Given information

Definition of a complex number

Begin by stating the given information

Equate like terms

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Measurements

Electrostatics

Famous Physicists

Modern Physics

Waves Physics

Oscillations

Study anywhere. Anytime. Across all devices.

Solve for all possible values of the real numbersand in the following equations ${(x + i y)}^{2} = {(x - i y)}^{2}$ .