Q40P - Mathematical Methods in Physical Sciences

Question

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

$\mathit{x}\mathbf{+}\mathit{i}\mathit{y}\mathbf{=}\mathbf{3}\mathit{i}\mathbf{-}\mathit{i}\mathit{x}$

Step-by-Step Solution

Answer

The answer is obtained:

 $x=0,y=3$

Step 1: Given information

It is given that $x+iy=3i-ix$

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 as:

 

$$\begin{gathered} x=iy=3i-ix \\ x+iy=0+i\left(3-x\right) \end{gathered}$$

Step 4: Equate like terms.

Equate like terms from both sides as:

 

$$\begin{gathered} x=0 \\ \mathrm{and} \\ y=3-x \\ y=3 \end{gathered}$$

 

Thus, the final answer is obtained:

 

$x=0,y=3$