Chapter 2: Q43P (page 54)

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

Short Answer

Expert verified

The answer is $(x, y) = (0, 0) o r (1, 1) o r (- 1, 1) .$

Step by step solution

Given information

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

Definition of a complex number

Every complex number can be described as:

z=a+bi

Where aand bare 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

State the given information as:

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

Equate like terms

Equate like terms from both sides:

$x^{2} - y^{2} = 0 x^{2} = y^{2} a n d x (y - 1) = 0$

Evaluate possible solutions

The above equation implies:

$I f x = 0 t h e n y = 0 I f y = 1 t h e n x = \pm 1$

Thus, the final answer is $(x, y) = (0, 0) o r (1, 1) o r (- 1, 1)$ .

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

Short Answer

Step by step solution

Given information

Definition of a complex number

Begin by stating the given information

Equate like terms

Evaluate possible solutions

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

Short Answer

Step by step solution

Given information

Definition of a complex number

Begin by stating the given information

Equate like terms

Evaluate possible solutions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Engineering Physics

Mechanics and Materials

Conservation of Energy and Momentum

Circular Motion and Gravitation

Thermodynamics

Astrophysics

Study anywhere. Anytime. Across all devices.

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