(3+2i)(a+bi)=16-11i

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Solution for (3+2i)(a+bi)=16-11i equation: 


Simplifying
(3 + 2i)(a + bi) = 16 + -11i

Multiply (3 + 2i) * (a + bi)
(3(a + bi) + 2i * (a + bi)) = 16 + -11i
((a * 3 + bi * 3) + 2i * (a + bi)) = 16 + -11i
((3a + 3bi) + 2i * (a + bi)) = 16 + -11i
(3a + 3bi + (a * 2i + bi * 2i)) = 16 + -11i
(3a + 3bi + (2ai + 2bi2)) = 16 + -11i

Reorder the terms:
(3a + 2ai + 3bi + 2bi2) = 16 + -11i
(3a + 2ai + 3bi + 2bi2) = 16 + -11i

Solving
3a + 2ai + 3bi + 2bi2 = 16 + -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 = 16 + -3bi + -11i

Combine like terms: 3bi + -3bi = 0
3a + 2ai + 0 + 2bi2 = 16 + -3bi + -11i
3a + 2ai + 2bi2 = 16 + -3bi + -11i

Add '-2bi2' to each side of the equation.
3a + 2ai + 2bi2 + -2bi2 = 16 + -3bi + -2bi2 + -11i

Combine like terms: 2bi2 + -2bi2 = 0
3a + 2ai + 0 = 16 + -3bi + -2bi2 + -11i
3a + 2ai = 16 + -3bi + -2bi2 + -11i

Reorder the terms:
-16 + 3a + 2ai + 3bi + 2bi2 + 11i = 16 + -3bi + -2bi2 + -11i + -16 + 3bi + 2bi2 + 11i

Reorder the terms:
-16 + 3a + 2ai + 3bi + 2bi2 + 11i = 16 + -16 + -3bi + 3bi + -2bi2 + 2bi2 + -11i + 11i

Combine like terms: 16 + -16 = 0
-16 + 3a + 2ai + 3bi + 2bi2 + 11i = 0 + -3bi + 3bi + -2bi2 + 2bi2 + -11i + 11i
-16 + 3a + 2ai + 3bi + 2bi2 + 11i = -3bi + 3bi + -2bi2 + 2bi2 + -11i + 11i

Combine like terms: -3bi + 3bi = 0
-16 + 3a + 2ai + 3bi + 2bi2 + 11i = 0 + -2bi2 + 2bi2 + -11i + 11i
-16 + 3a + 2ai + 3bi + 2bi2 + 11i = -2bi2 + 2bi2 + -11i + 11i

Combine like terms: -2bi2 + 2bi2 = 0
-16 + 3a + 2ai + 3bi + 2bi2 + 11i = 0 + -11i + 11i
-16 + 3a + 2ai + 3bi + 2bi2 + 11i = -11i + 11i

Combine like terms: -11i + 11i = 0
-16 + 3a + 2ai + 3bi + 2bi2 + 11i = 0

The solution to this equation could not be determined.

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