5-4i=(a+3)+(b-1)i

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Solution for 5-4i=(a+3)+(b-1)i equation: 


Simplifying
5 + -4i = (a + 3) + (b + -1) * i

Reorder the terms:
5 + -4i = (3 + a) + (b + -1) * i

Remove parenthesis around (3 + a)
5 + -4i = 3 + a + (b + -1) * i

Reorder the terms:
5 + -4i = 3 + a + (-1 + b) * i

Reorder the terms for easier multiplication:
5 + -4i = 3 + a + i(-1 + b)
5 + -4i = 3 + a + (-1 * i + b * i)

Reorder the terms:
5 + -4i = 3 + a + (bi + -1i)
5 + -4i = 3 + a + (bi + -1i)

Solving
5 + -4i = 3 + a + bi + -1i

Solving for variable 'i'.

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

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

Combine like terms: bi + -1bi = 0
5 + -1bi + -4i = 3 + a + 0 + -1i
5 + -1bi + -4i = 3 + a + -1i

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

Combine like terms: -4i + i = -3i
5 + -1bi + -3i = 3 + a + -1i + i

Combine like terms: -1i + i = 0
5 + -1bi + -3i = 3 + a + 0
5 + -1bi + -3i = 3 + a

Add '-5' to each side of the equation.
5 + -1bi + -5 + -3i = 3 + -5 + a

Reorder the terms:
5 + -5 + -1bi + -3i = 3 + -5 + a

Combine like terms: 5 + -5 = 0
0 + -1bi + -3i = 3 + -5 + a
-1bi + -3i = 3 + -5 + a

Combine like terms: 3 + -5 = -2
-1bi + -3i = -2 + a

Reorder the terms:
2 + -1a + -1bi + -3i = -2 + a + 2 + -1a

Reorder the terms:
2 + -1a + -1bi + -3i = -2 + 2 + a + -1a

Combine like terms: -2 + 2 = 0
2 + -1a + -1bi + -3i = 0 + a + -1a
2 + -1a + -1bi + -3i = a + -1a

Combine like terms: a + -1a = 0
2 + -1a + -1bi + -3i = 0

The solution to this equation could not be determined.

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