(3+2i)(a+bi)=-3+11i

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Solution for (3+2i)(a+bi)=-3+11i equation: 


Simplifying
(3 + 2i)(a + bi) = -3 + 11i

Multiply (3 + 2i) * (a + bi)
(3(a + bi) + 2i * (a + bi)) = -3 + 11i
((a * 3 + bi * 3) + 2i * (a + bi)) = -3 + 11i
((3a + 3bi) + 2i * (a + bi)) = -3 + 11i
(3a + 3bi + (a * 2i + bi * 2i)) = -3 + 11i
(3a + 3bi + (2ai + 2bi2)) = -3 + 11i

Reorder the terms:
(3a + 2ai + 3bi + 2bi2) = -3 + 11i
(3a + 2ai + 3bi + 2bi2) = -3 + 11i

Solving
3a + 2ai + 3bi + 2bi2 = -3 + 11i

Solving for variable 'a'.

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

Add '-3bi' to each side of the equation.
3a + 2ai + 3bi + -3bi + 2bi2 = -3 + -3bi + 11i

Combine like terms: 3bi + -3bi = 0
3a + 2ai + 0 + 2bi2 = -3 + -3bi + 11i
3a + 2ai + 2bi2 = -3 + -3bi + 11i

Add '-2bi2' to each side of the equation.
3a + 2ai + 2bi2 + -2bi2 = -3 + -3bi + -2bi2 + 11i

Combine like terms: 2bi2 + -2bi2 = 0
3a + 2ai + 0 = -3 + -3bi + -2bi2 + 11i
3a + 2ai = -3 + -3bi + -2bi2 + 11i

Reorder the terms:
3 + 3a + 2ai + 3bi + 2bi2 + -11i = -3 + -3bi + -2bi2 + 11i + 3 + 3bi + 2bi2 + -11i

Reorder the terms:
3 + 3a + 2ai + 3bi + 2bi2 + -11i = -3 + 3 + -3bi + 3bi + -2bi2 + 2bi2 + 11i + -11i

Combine like terms: -3 + 3 = 0
3 + 3a + 2ai + 3bi + 2bi2 + -11i = 0 + -3bi + 3bi + -2bi2 + 2bi2 + 11i + -11i
3 + 3a + 2ai + 3bi + 2bi2 + -11i = -3bi + 3bi + -2bi2 + 2bi2 + 11i + -11i

Combine like terms: -3bi + 3bi = 0
3 + 3a + 2ai + 3bi + 2bi2 + -11i = 0 + -2bi2 + 2bi2 + 11i + -11i
3 + 3a + 2ai + 3bi + 2bi2 + -11i = -2bi2 + 2bi2 + 11i + -11i

Combine like terms: -2bi2 + 2bi2 = 0
3 + 3a + 2ai + 3bi + 2bi2 + -11i = 0 + 11i + -11i
3 + 3a + 2ai + 3bi + 2bi2 + -11i = 11i + -11i

Combine like terms: 11i + -11i = 0
3 + 3a + 2ai + 3bi + 2bi2 + -11i = 0

The solution to this equation could not be determined.

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