Question

Solve for all possible values of the real numbers x and y in the following equations.$\mathbf{|}\mathbf{x}\mathbf{+}\mathbf{i}\mathbf{y}\mathbf{|}\mathbf{=}\mathit{y}\mathbf{-}\mathit{i}\mathit{x}\mathbf{.}$ .

Short answer

The possible values are given below:

$x=0,y\ge 0$

Step-by-step solution

Given Information 

The equation is$|x+iy|=y-ix.$ .

Definition of the Complex number

Every complex number can be represented as:

z=a+bi

Where aand b are both real numbers, z is the complex number, and i is known as iota, which makes z a complex number.

Find the values

The equation is $\left|x+yi\right|=y-xi.$.

The value of the modulus must be real and positive so, $x=0$.

Now the above equation can be written as:

$y=\left|iy\right|$

Hence, it satisfies all the values of any real positive number.

The possible values are given below:

$x=0,y\ge 0$