(5+4i)-(x+yi)=(-1-3i)

Solution for (5+4i)-(x+yi)=(-1-3i) equation:

Simplifying
(5 + 4i) + -1(x + yi) = (-1 + -3i)

Remove parenthesis around (5 + 4i)
5 + 4i + -1(x + yi) = (-1 + -3i)

Reorder the terms:
5 + 4i + -1(iy + x) = (-1 + -3i)
5 + 4i + (iy * -1 + x * -1) = (-1 + -3i)
5 + 4i + (-1iy + -1x) = (-1 + -3i)

Remove parenthesis around (-1 + -3i)
5 + 4i + -1iy + -1x = -1 + -3i

Solving
5 + 4i + -1iy + -1x = -1 + -3i

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '3i' to each side of the equation.
5 + 4i + -1iy + 3i + -1x = -1 + -3i + 3i

Reorder the terms:
5 + 4i + 3i + -1iy + -1x = -1 + -3i + 3i

Combine like terms: 4i + 3i = 7i
5 + 7i + -1iy + -1x = -1 + -3i + 3i

Combine like terms: -3i + 3i = 0
5 + 7i + -1iy + -1x = -1 + 0
5 + 7i + -1iy + -1x = -1

Add '-5' to each side of the equation.
5 + 7i + -1iy + -5 + -1x = -1 + -5

Reorder the terms:
5 + -5 + 7i + -1iy + -1x = -1 + -5

Combine like terms: 5 + -5 = 0
0 + 7i + -1iy + -1x = -1 + -5
7i + -1iy + -1x = -1 + -5

Combine like terms: -1 + -5 = -6
7i + -1iy + -1x = -6

Add 'x' to each side of the equation.
7i + -1iy + -1x + x = -6 + x

Combine like terms: -1x + x = 0
7i + -1iy + 0 = -6 + x
7i + -1iy = -6 + x

Reorder the terms:
6 + 7i + -1iy + -1x = -6 + x + 6 + -1x

Reorder the terms:
6 + 7i + -1iy + -1x = -6 + 6 + x + -1x

Combine like terms: -6 + 6 = 0
6 + 7i + -1iy + -1x = 0 + x + -1x
6 + 7i + -1iy + -1x = x + -1x

Combine like terms: x + -1x = 0
6 + 7i + -1iy + -1x = 0

The solution to this equation could not be determined.