Question

Solve for all possible values of the real numbersand 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$a$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:

$2ix+3=y-i$

Equate like terms

Equate like terms from both sides as:

$$\begin{gathered} 2ix+3=y-i \\ 2x=-1 \\ x=-\frac{1}{2} \\ \mathrm{and} \\ \mathrm{y}=3 \end{gathered}$$

Thus, the final answer is obtained as:

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