4(a+bi)(a+bi)+8(a+bi)(a-bi)-3=0

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Solution for 4(a+bi)(a+bi)+8(a+bi)(a-bi)-3=0 equation: 


Simplifying
4(a + bi)(a + bi) + 8(a + bi)(a + -1bi) + -3 = 0

Multiply (a + bi) * (a + bi)
4(a(a + bi) + bi(a + bi)) + 8(a + bi)(a + -1bi) + -3 = 0
4((a * a + bi * a) + bi(a + bi)) + 8(a + bi)(a + -1bi) + -3 = 0

Reorder the terms:
4((abi + a2) + bi(a + bi)) + 8(a + bi)(a + -1bi) + -3 = 0
4((abi + a2) + bi(a + bi)) + 8(a + bi)(a + -1bi) + -3 = 0
4(abi + a2 + (a * bi + bi * bi)) + 8(a + bi)(a + -1bi) + -3 = 0
4(abi + a2 + (abi + b2i2)) + 8(a + bi)(a + -1bi) + -3 = 0

Reorder the terms:
4(abi + abi + a2 + b2i2) + 8(a + bi)(a + -1bi) + -3 = 0

Combine like terms: abi + abi = 2abi
4(2abi + a2 + b2i2) + 8(a + bi)(a + -1bi) + -3 = 0
(2abi * 4 + a2 * 4 + b2i2 * 4) + 8(a + bi)(a + -1bi) + -3 = 0
(8abi + 4a2 + 4b2i2) + 8(a + bi)(a + -1bi) + -3 = 0

Multiply (a + bi) * (a + -1bi)
8abi + 4a2 + 4b2i2 + 8(a(a + -1bi) + bi(a + -1bi)) + -3 = 0
8abi + 4a2 + 4b2i2 + 8((a * a + -1bi * a) + bi(a + -1bi)) + -3 = 0

Reorder the terms:
8abi + 4a2 + 4b2i2 + 8((-1abi + a2) + bi(a + -1bi)) + -3 = 0
8abi + 4a2 + 4b2i2 + 8((-1abi + a2) + bi(a + -1bi)) + -3 = 0
8abi + 4a2 + 4b2i2 + 8(-1abi + a2 + (a * bi + -1bi * bi)) + -3 = 0
8abi + 4a2 + 4b2i2 + 8(-1abi + a2 + (abi + -1b2i2)) + -3 = 0

Reorder the terms:
8abi + 4a2 + 4b2i2 + 8(-1abi + abi + a2 + -1b2i2) + -3 = 0

Combine like terms: -1abi + abi = 0
8abi + 4a2 + 4b2i2 + 8(0 + a2 + -1b2i2) + -3 = 0
8abi + 4a2 + 4b2i2 + 8(a2 + -1b2i2) + -3 = 0
8abi + 4a2 + 4b2i2 + (a2 * 8 + -1b2i2 * 8) + -3 = 0
8abi + 4a2 + 4b2i2 + (8a2 + -8b2i2) + -3 = 0

Reorder the terms:
-3 + 8abi + 4a2 + 8a2 + 4b2i2 + -8b2i2 = 0

Combine like terms: 4a2 + 8a2 = 12a2
-3 + 8abi + 12a2 + 4b2i2 + -8b2i2 = 0

Combine like terms: 4b2i2 + -8b2i2 = -4b2i2
-3 + 8abi + 12a2 + -4b2i2 = 0

Solving
-3 + 8abi + 12a2 + -4b2i2 = 0

Solving for variable 'a'.

The solution to this equation could not be determined.

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