Q39P - Mathematical Methods in Physical Sciences

Question

Solve for all possible values of the real numbers $\mathit{x}$ and $\mathit{y}$in the following equations.

$\mathit{x}\mathbf{+}\mathit{i}\mathit{y}\mathbf{=}\mathit{y}\mathbf{+}\mathit{i}\mathit{x}$

Step-by-Step Solution

Answer

The answer is obtained:

$x=y=\mathrm{any} \mathrm{real} \mathrm{number}$

Step 1: Given information

It is given that $x+iy=y+ix$.

Step 2: Definition of a complex number

Every complex number can be expressed as: 

 

z=a+bi

Where$a$and$b$are both real numbers, z is the complex number, and i is known as iota, which makes z a complex number.

Step 3: Begin by stating the given information

State the given information:

 

$x+iy=y+ix$

Step 4: Equate like terms

Equate like terms from both sides:

 

$$\begin{gathered} x+iy=y+ix \\ x=y \\ \mathrm{and} \\ \mathrm{y}=\mathrm{x} \end{gathered}$$

 

Thus, the final answer is obtained:

$x=y=\mathrm{any} \mathrm{real} \mathrm{number}$