x+ 2i + y = x*i + 6 - yi

First let us group temrs with x and y on the left side:

x+ y - x*i + y*i = 6 - 2i

(x+y) + (y-x)*i = 6 - 2i

==> x+ y = 6 .........(1)

==> y - x = -2 ........(2)

Using the elimination method, add (1) and (2)

==> 2y = 4

==>** y= 2**

Now to calculate x, substitute in (1);

x+ y = 6 ==> x= 6-y = 6- 2= 4

==> **x= 4**

**Ten the solution is:**

**x= 4 and y=2**

To determine x and y, we'll group, both sides, the real parts and the imaginary parts.

To the left side, the real part is (x+y) and the imaginary part is 2.

(x+y) + 2i = 6 + i*(x-y)

We'll put the real part from the left side equal to the real part from the right side:

x+y = 6 (1)

We'll put the imaginary part from the left side equal to the imaginary part from the right side:

x - y = 2 (2)

We'll add (1)+(2):

x+y+x-y = 6+2

We'll eliminate like terms:

2x = 8

**x = 4**

We'll substitute x=4 into (1):

x+y = 6

4+y = 6

y = 6-4

**y = 2**

x+2i+y=x*i+6-y*i..

To find x and y.

Solution:

We rewrite the given equation real variables(or unknowns x or y) and imaginary variables( x or y) on left and real knowns and imaginary knowns on right as below:

(x+y) - xi+yi = 6-2i

(x+y) +(y-x)i = 6-2i. Now equate reals on both sides. And equate imaginaries on both sides:

x+y = 6 and y-x = -2. Adding these eqations: 2y = 6-2 =4, y = 2.

Subtracting, 2x = 6- -2 = 8, x = 4.

Therefore x = 4 and y = 2.

A