(3a-2i)(a+bi)=18+i

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Solution for (3a-2i)(a+bi)=18+i equation: 


Simplifying
(3a + -2i)(a + bi) = 18 + i

Multiply (3a + -2i) * (a + bi)
(3a * (a + bi) + -2i * (a + bi)) = 18 + i
((a * 3a + bi * 3a) + -2i * (a + bi)) = 18 + i

Reorder the terms:
((3abi + 3a2) + -2i * (a + bi)) = 18 + i
((3abi + 3a2) + -2i * (a + bi)) = 18 + i
(3abi + 3a2 + (a * -2i + bi * -2i)) = 18 + i
(3abi + 3a2 + (-2ai + -2bi2)) = 18 + i

Reorder the terms:
(3abi + -2ai + 3a2 + -2bi2) = 18 + i
(3abi + -2ai + 3a2 + -2bi2) = 18 + i

Solving
3abi + -2ai + 3a2 + -2bi2 = 18 + i

Solving for variable 'a'.

Reorder the terms:
-18 + 3abi + -2ai + 3a2 + -2bi2 + -1i = 18 + i + -18 + -1i

Reorder the terms:
-18 + 3abi + -2ai + 3a2 + -2bi2 + -1i = 18 + -18 + i + -1i

Combine like terms: 18 + -18 = 0
-18 + 3abi + -2ai + 3a2 + -2bi2 + -1i = 0 + i + -1i
-18 + 3abi + -2ai + 3a2 + -2bi2 + -1i = i + -1i

Combine like terms: i + -1i = 0
-18 + 3abi + -2ai + 3a2 + -2bi2 + -1i = 0

The solution to this equation could not be determined.

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