(3x-1)+(y+5)i=1-3i

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


Simplifying
(3x + -1) + (y + 5) * i = 1 + -3i

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

Remove parenthesis around (-1 + 3x)
-1 + 3x + (y + 5) * i = 1 + -3i

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

Reorder the terms for easier multiplication:
-1 + 3x + i(5 + y) = 1 + -3i
-1 + 3x + (5 * i + y * i) = 1 + -3i
-1 + 3x + (5i + iy) = 1 + -3i

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

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

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

Combine like terms: 5i + 3i = 8i
-1 + 8i + iy + 3x = 1 + -3i + 3i

Combine like terms: -3i + 3i = 0
-1 + 8i + iy + 3x = 1 + 0
-1 + 8i + iy + 3x = 1

Add '1' to each side of the equation.
-1 + 8i + iy + 1 + 3x = 1 + 1

Reorder the terms:
-1 + 1 + 8i + iy + 3x = 1 + 1

Combine like terms: -1 + 1 = 0
0 + 8i + iy + 3x = 1 + 1
8i + iy + 3x = 1 + 1

Combine like terms: 1 + 1 = 2
8i + iy + 3x = 2

Add '-3x' to each side of the equation.
8i + iy + 3x + -3x = 2 + -3x

Combine like terms: 3x + -3x = 0
8i + iy + 0 = 2 + -3x
8i + iy = 2 + -3x

Reorder the terms:
-2 + 8i + iy + 3x = 2 + -3x + -2 + 3x

Reorder the terms:
-2 + 8i + iy + 3x = 2 + -2 + -3x + 3x

Combine like terms: 2 + -2 = 0
-2 + 8i + iy + 3x = 0 + -3x + 3x
-2 + 8i + iy + 3x = -3x + 3x

Combine like terms: -3x + 3x = 0
-2 + 8i + iy + 3x = 0

The solution to this equation could not be determined.

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