(a+3)+(2b-1)i=4-8i

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Solution for (a+3)+(2b-1)i=4-8i equation:


Simplifying
(a + 3) + (2b + -1) * i = 4 + -8i

Reorder the terms:
(3 + a) + (2b + -1) * i = 4 + -8i

Remove parenthesis around (3 + a)
3 + a + (2b + -1) * i = 4 + -8i

Reorder the terms:
3 + a + (-1 + 2b) * i = 4 + -8i

Reorder the terms for easier multiplication:
3 + a + i(-1 + 2b) = 4 + -8i
3 + a + (-1 * i + 2b * i) = 4 + -8i

Reorder the terms:
3 + a + (2bi + -1i) = 4 + -8i
3 + a + (2bi + -1i) = 4 + -8i

Solving
3 + a + 2bi + -1i = 4 + -8i

Solving for variable 'a'.

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

Add '-3' to each side of the equation.
3 + a + 2bi + -3 + -1i = 4 + -3 + -8i

Reorder the terms:
3 + -3 + a + 2bi + -1i = 4 + -3 + -8i

Combine like terms: 3 + -3 = 0
0 + a + 2bi + -1i = 4 + -3 + -8i
a + 2bi + -1i = 4 + -3 + -8i

Combine like terms: 4 + -3 = 1
a + 2bi + -1i = 1 + -8i

Add '-2bi' to each side of the equation.
a + 2bi + -2bi + -1i = 1 + -2bi + -8i

Combine like terms: 2bi + -2bi = 0
a + 0 + -1i = 1 + -2bi + -8i
a + -1i = 1 + -2bi + -8i

Add 'i' to each side of the equation.
a + -1i + i = 1 + -2bi + -8i + i

Combine like terms: -1i + i = 0
a + 0 = 1 + -2bi + -8i + i
a = 1 + -2bi + -8i + i

Combine like terms: -8i + i = -7i
a = 1 + -2bi + -7i

Simplifying
a = 1 + -2bi + -7i

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