2*(a+bi)-i*(a-bi)=2-2i

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Solution for 2*(a+bi)-i*(a-bi)=2-2i equation: 


Simplifying
2(a + bi) + -1i(a + -1bi) = 2 + -2i
(a * 2 + bi * 2) + -1i(a + -1bi) = 2 + -2i
(2a + 2bi) + -1i(a + -1bi) = 2 + -2i
2a + 2bi + (a * -1i + -1bi * -1i) = 2 + -2i
2a + 2bi + (-1ai + 1bi2) = 2 + -2i

Reorder the terms:
2a + -1ai + 2bi + 1bi2 = 2 + -2i

Solving
2a + -1ai + 2bi + 1bi2 = 2 + -2i

Solving for variable 'a'.

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

Add '-2bi' to each side of the equation.
2a + -1ai + 2bi + -2bi + 1bi2 = 2 + -2bi + -2i

Combine like terms: 2bi + -2bi = 0
2a + -1ai + 0 + 1bi2 = 2 + -2bi + -2i
2a + -1ai + 1bi2 = 2 + -2bi + -2i

Add '-1bi2' to each side of the equation.
2a + -1ai + 1bi2 + -1bi2 = 2 + -2bi + -1bi2 + -2i

Combine like terms: 1bi2 + -1bi2 = 0
2a + -1ai + 0 = 2 + -2bi + -1bi2 + -2i
2a + -1ai = 2 + -2bi + -1bi2 + -2i

Reorder the terms:
-2 + 2a + -1ai + 2bi + bi2 + 2i = 2 + -2bi + -1bi2 + -2i + -2 + 2bi + bi2 + 2i

Reorder the terms:
-2 + 2a + -1ai + 2bi + bi2 + 2i = 2 + -2 + -2bi + 2bi + -1bi2 + bi2 + -2i + 2i

Combine like terms: 2 + -2 = 0
-2 + 2a + -1ai + 2bi + bi2 + 2i = 0 + -2bi + 2bi + -1bi2 + bi2 + -2i + 2i
-2 + 2a + -1ai + 2bi + bi2 + 2i = -2bi + 2bi + -1bi2 + bi2 + -2i + 2i

Combine like terms: -2bi + 2bi = 0
-2 + 2a + -1ai + 2bi + bi2 + 2i = 0 + -1bi2 + bi2 + -2i + 2i
-2 + 2a + -1ai + 2bi + bi2 + 2i = -1bi2 + bi2 + -2i + 2i

Combine like terms: -1bi2 + bi2 = 0
-2 + 2a + -1ai + 2bi + bi2 + 2i = 0 + -2i + 2i
-2 + 2a + -1ai + 2bi + bi2 + 2i = -2i + 2i

Combine like terms: -2i + 2i = 0
-2 + 2a + -1ai + 2bi + bi2 + 2i = 0

The solution to this equation could not be determined.

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