(a+i)(4-bi)=3b+2ai

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Solution for (a+i)(4-bi)=3b+2ai equation: 


Simplifying
(a + i)(4 + -1bi) = 3b + 2ai

Multiply (a + i) * (4 + -1bi)
(a(4 + -1bi) + i(4 + -1bi)) = 3b + 2ai
((4 * a + -1bi * a) + i(4 + -1bi)) = 3b + 2ai
((4a + -1abi) + i(4 + -1bi)) = 3b + 2ai
(4a + -1abi + (4 * i + -1bi * i)) = 3b + 2ai

Reorder the terms:
(4a + -1abi + (-1bi2 + 4i)) = 3b + 2ai
(4a + -1abi + (-1bi2 + 4i)) = 3b + 2ai
(4a + -1abi + -1bi2 + 4i) = 3b + 2ai

Reorder the terms:
4a + -1abi + -1bi2 + 4i = 2ai + 3b

Solving
4a + -1abi + -1bi2 + 4i = 2ai + 3b

Solving for variable 'a'.

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

Add '-2ai' to each side of the equation.
4a + -1abi + -1bi2 + -2ai + 4i = 2ai + -2ai + 3b

Reorder the terms:
4a + -1abi + -2ai + -1bi2 + 4i = 2ai + -2ai + 3b

Combine like terms: 2ai + -2ai = 0
4a + -1abi + -2ai + -1bi2 + 4i = 0 + 3b
4a + -1abi + -2ai + -1bi2 + 4i = 3b

Add 'bi2' to each side of the equation.
4a + -1abi + -2ai + -1bi2 + bi2 + 4i = 3b + bi2

Combine like terms: -1bi2 + bi2 = 0
4a + -1abi + -2ai + 0 + 4i = 3b + bi2
4a + -1abi + -2ai + 4i = 3b + bi2

Add '-4i' to each side of the equation.
4a + -1abi + -2ai + 4i + -4i = 3b + bi2 + -4i

Combine like terms: 4i + -4i = 0
4a + -1abi + -2ai + 0 = 3b + bi2 + -4i
4a + -1abi + -2ai = 3b + bi2 + -4i

Reorder the terms:
4a + -1abi + -2ai + -3b + -1bi2 + 4i = 3b + -3b + bi2 + -1bi2 + -4i + 4i

Combine like terms: 3b + -3b = 0
4a + -1abi + -2ai + -3b + -1bi2 + 4i = 0 + bi2 + -1bi2 + -4i + 4i
4a + -1abi + -2ai + -3b + -1bi2 + 4i = bi2 + -1bi2 + -4i + 4i

Combine like terms: bi2 + -1bi2 = 0
4a + -1abi + -2ai + -3b + -1bi2 + 4i = 0 + -4i + 4i
4a + -1abi + -2ai + -3b + -1bi2 + 4i = -4i + 4i

Combine like terms: -4i + 4i = 0
4a + -1abi + -2ai + -3b + -1bi2 + 4i = 0

The solution to this equation could not be determined.

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