Question

Solve for all possible values of the real numbers xand y in the following equations.

$\mathbf{2}\mathit{i}\mathit{x}\mathbf{+}\mathbf{3}\mathbf{=}\mathit{y}\mathbf{-}\mathit{i}$

Short answer

The answer is obtained as:

$x=-\frac{1}{2},y=3$

Step-by-step solution

Given information

It is given that 2ix + 3 = y - i .

Definition of a complex number

Every complex number can be written as:

z = a + bi

Where aand bare 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:

2ix + 3 = y - i

Equate like terms

Equate like terms from both sides as:

$$\begin{gathered} 2\mathrm{ix}+3=\mathrm{y}-\mathrm{i} \\ 2\mathrm{x}=-1 \\ \mathrm{x}=-\frac{1}{2} \\ \mathrm{and} \\ \mathrm{y}=3 \\ \mathrm{Thus},\mathrm{the}\mathrm{final}\mathrm{answer}\mathrm{is}\mathrm{obtained}\mathrm{as}: \\ \mathrm{x}=-\frac{1}{2},\mathrm{y}=3 \end{gathered}$$