Chapter 2: Q42P (page 54)

Solve for all possible values of the real numbers $x$ and $y$ in the following equations. $(x + 2 y + 3) + i (3 x - y - 1) = 0$

Short Answer

Expert verified

The answer is obtained:

$x = - \frac{1}{7}, y = - \frac{10}{7}$

Step by step solution

Given information

It is given that $(x + 2 y + 3) + i (3 x - y - 1) = 0$ .

Definition of a complex number

Every complex number can be expressed as:

$z = a + b i$

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

State the given information:

$(x + 2 y + 3) + i (3 x - y - 1) = 0$

Equate like terms

Equate like terms from both sides as:

$x + 2 y = - 3 3 x - y = 1$

Solve the two equations to find the solutions

Multiply the second equation by $2$ and add it to the first equation as:

$x + 2 y = - 3 6 x - 2 y = 2$

Continue evaluation:

$7 x = - 1 x = - \frac{1}{7} and y = 3 x - 1 y = 3 (- \frac{1}{7}) - 1 y = - \frac{3}{7} - 1 y = - \frac{10}{7}$

Thus, the final answer is obtained:

$x = - \frac{1}{7}, y = - \frac{10}{7}$

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Solve for all possible values of the real numbers $x$ and $y$ in the following equations. $(x + 2 y + 3) + i (3 x - y - 1) = 0$

Short Answer

Step by step solution

Given information

Definition of a complex number

Begin by stating the given information

Equate like terms

Solve the two equations to find the solutions

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Most popular questions from this chapter

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Solve for all possible values of the real numbers xand yin the following equations.(x+2y+3)+i(3x-y-1)=0

Short Answer

Step by step solution

Given information

Definition of a complex number

Begin by stating the given information

Equate like terms

Solve the two equations to find the solutions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fields in Physics

Torque and Rotational Motion

Linear Momentum

Nuclear Physics

Electricity and Magnetism

Electrostatics

Study anywhere. Anytime. Across all devices.

Solve for all possible values of the real numbers $x$ and $y$ in the following equations. $(x + 2 y + 3) + i (3 x - y - 1) = 0$