Q37P - Mathematical Methods in Physical Sciences

Question

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

$\mathit{x}\mathbf{+}\mathit{i}\mathit{y}\mathbf{=}\mathbf{0}$

Step-by-Step Solution

Answer

The answer is obtained as:

$x=0,y=0$

Step 1: Given information

It is given that $x+iy=0$.

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:

 

$x+iy=0$

Step 4: Equate like terms

Equate like terms from both sides as:

 

$$\begin{gathered} x+iy=0 \\ x=0 \\ \mathrm{and} \\ \mathrm{y}=0 \end{gathered}$$

 

Thus, the final answer is obtained:

 $x=0,y=0$