Q38P - Mathematical Methods in Physical Sciences

Question

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

$\mathit{x}\mathbf{+}\mathit{i}\mathit{y}\mathbf{=}\mathbf{2}\mathit{i}\mathbf{-}\mathbf{7}$

Step-by-Step Solution

Answer

The answer is obtained:

$x=-7,y=2$

Step 1: Given information

It is given that $x+iy=2i-7$.

Step 2: 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.

Step 3: Begin by stating the given information

State the given information as:

 

$x+iy=2i-7$

Step 4: Equate like terms

Equate like terms from both sides as:

 

$$\begin{gathered} x+iy=2i-7 \\ x=-7 \\ \mathrm{and} \\ \mathrm{y}=2 \end{gathered}$$

 

Thus, the final answer is obtained:

 $x=-7,y=2$