12-5i=(a+2)+(b-1)i

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Solution for 12-5i=(a+2)+(b-1)i equation: 


Simplifying
12 + -5i = (a + 2) + (b + -1) * i

Reorder the terms:
12 + -5i = (2 + a) + (b + -1) * i

Remove parenthesis around (2 + a)
12 + -5i = 2 + a + (b + -1) * i

Reorder the terms:
12 + -5i = 2 + a + (-1 + b) * i

Reorder the terms for easier multiplication:
12 + -5i = 2 + a + i(-1 + b)
12 + -5i = 2 + a + (-1 * i + b * i)

Reorder the terms:
12 + -5i = 2 + a + (bi + -1i)
12 + -5i = 2 + a + (bi + -1i)

Solving
12 + -5i = 2 + 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.
12 + -1bi + -5i = 2 + a + bi + -1bi + -1i

Combine like terms: bi + -1bi = 0
12 + -1bi + -5i = 2 + a + 0 + -1i
12 + -1bi + -5i = 2 + a + -1i

Add 'i' to each side of the equation.
12 + -1bi + -5i + i = 2 + a + -1i + i

Combine like terms: -5i + i = -4i
12 + -1bi + -4i = 2 + a + -1i + i

Combine like terms: -1i + i = 0
12 + -1bi + -4i = 2 + a + 0
12 + -1bi + -4i = 2 + a

Add '-12' to each side of the equation.
12 + -1bi + -12 + -4i = 2 + -12 + a

Reorder the terms:
12 + -12 + -1bi + -4i = 2 + -12 + a

Combine like terms: 12 + -12 = 0
0 + -1bi + -4i = 2 + -12 + a
-1bi + -4i = 2 + -12 + a

Combine like terms: 2 + -12 = -10
-1bi + -4i = -10 + a

Reorder the terms:
10 + -1a + -1bi + -4i = -10 + a + 10 + -1a

Reorder the terms:
10 + -1a + -1bi + -4i = -10 + 10 + a + -1a

Combine like terms: -10 + 10 = 0
10 + -1a + -1bi + -4i = 0 + a + -1a
10 + -1a + -1bi + -4i = a + -1a

Combine like terms: a + -1a = 0
10 + -1a + -1bi + -4i = 0

The solution to this equation could not be determined.

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