(a+bi)(a-bi)-4i(a-bi)=4-8i

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Solution for (a+bi)(a-bi)-4i(a-bi)=4-8i equation: 


Simplifying
(a + bi)(a + -1bi) + -4i(a + -1bi) = 4 + -8i

Multiply (a + bi) * (a + -1bi)
(a(a + -1bi) + bi(a + -1bi)) + -4i(a + -1bi) = 4 + -8i
((a * a + -1bi * a) + bi(a + -1bi)) + -4i(a + -1bi) = 4 + -8i

Reorder the terms:
((-1abi + a2) + bi(a + -1bi)) + -4i(a + -1bi) = 4 + -8i
((-1abi + a2) + bi(a + -1bi)) + -4i(a + -1bi) = 4 + -8i
(-1abi + a2 + (a * bi + -1bi * bi)) + -4i(a + -1bi) = 4 + -8i
(-1abi + a2 + (abi + -1b2i2)) + -4i(a + -1bi) = 4 + -8i

Reorder the terms:
(-1abi + abi + a2 + -1b2i2) + -4i(a + -1bi) = 4 + -8i

Combine like terms: -1abi + abi = 0
(0 + a2 + -1b2i2) + -4i(a + -1bi) = 4 + -8i
(a2 + -1b2i2) + -4i(a + -1bi) = 4 + -8i
a2 + -1b2i2 + (a * -4i + -1bi * -4i) = 4 + -8i
a2 + -1b2i2 + (-4ai + 4bi2) = 4 + -8i

Reorder the terms:
-4ai + a2 + 4bi2 + -1b2i2 = 4 + -8i

Solving
-4ai + a2 + 4bi2 + -1b2i2 = 4 + -8i

Solving for variable 'a'.

Reorder the terms:
-4 + -4ai + a2 + 4bi2 + -1b2i2 + 8i = 4 + -8i + -4 + 8i

Reorder the terms:
-4 + -4ai + a2 + 4bi2 + -1b2i2 + 8i = 4 + -4 + -8i + 8i

Combine like terms: 4 + -4 = 0
-4 + -4ai + a2 + 4bi2 + -1b2i2 + 8i = 0 + -8i + 8i
-4 + -4ai + a2 + 4bi2 + -1b2i2 + 8i = -8i + 8i

Combine like terms: -8i + 8i = 0
-4 + -4ai + a2 + 4bi2 + -1b2i2 + 8i = 0

The solution to this equation could not be determined.

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