Question

Solve for all possible values of the real numbers xand y in the following equations.$\mathit{x}\mathbf{+}\mathit{i}\mathit{y}\mathbf{=}{\left(1-i\right)}^{\mathbf{2}}$

Short answer

The answer is obtained:

$x=0,y=-2$

Step-by-step solution

Given information

It is given that $x+iy={\left(1-i\right)}^2$.

Definition of a complex number

Every complex number can be described as:

z=a+bi

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:

$x+iy={\left(1-i\right)}^2$

Equate like terms

Equate like terms from both sides:

$$\begin{gathered} x-iy={\left(1-i\right)}^2 \\ x-iy=1-2i-1 \\ x+iy=-2i \end{gathered}$$

Solve it further as:

$$\begin{gathered} x=0 \\ and \\ y=-2 \end{gathered}$$

Thus, the final answer is obtained:

$x=0,y=-2$