Q35P - Mathematical Methods in Physical Sciences

Question

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

 $\mathit{x}\mathbf{+}\mathit{i}\mathit{y}\mathbf{=}\mathbf{3}\mathit{i}\mathbf{-}\mathbf{4}$

Step-by-Step Solution

Answer

The answer is obtained as: $x=-4,y=3$ .

Step 1: Given information

It is given that $x+iy=3i-4$ .

Step 2: Definition of a complex number

Every complex number can be written as: 

 

 $z=a+bi$

 

Where   and   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:

$x=iy=3i-4$ 

Step 4: Equate like terms

Equate like terms from both sides as:

 

 $$\begin{gathered} x=-4 \\ \mathrm{and} \\ y=3 \end{gathered}$$

 

Thus, the final answer is obtained:

 $x=-4,y=3$