Question

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

$\mathit{x}\mathbf{+}\mathit{i}\mathit{y}\mathbf{=}\mathbf{0}$

Short answer

The answer is obtained as:

$x=0,y=0$

Step-by-step solution

Given information

It is given that $x+iy=0$.

Definition of a complex number

Every complex number can be written 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.

Begin by stating the given information

State the given information as:

$x+iy=0$

Equate like terms

Equate like terms from both sides as:

$$\begin{gathered} x+iy=0 \\ x=0 \\ \mathrm{and} \\ \mathrm{y}=0 \end{gathered}$$

Thus, the final answer is obtained:

$x=0,y=0$