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Simplifying x + 6y + (x + y) * I = 3 + 8i Reorder the terms for easier multiplication: x + 6y + I(x + y) = 3 + 8i x + 6y + (x * I + y * I) = 3 + 8i x + 6y + (xI + yI) = 3 + 8i Reorder the terms: x + xI + 6y + yI = 3 + 8i Solving x + xI + 6y + yI = 3 + 8i Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6y' to each side of the equation. x + xI + 6y + -6y + yI = 3 + 8i + -6y Combine like terms: 6y + -6y = 0 x + xI + 0 + yI = 3 + 8i + -6y x + xI + yI = 3 + 8i + -6y Add '-1yI' to each side of the equation. x + xI + yI + -1yI = 3 + 8i + -6y + -1yI Combine like terms: yI + -1yI = 0 x + xI + 0 = 3 + 8i + -6y + -1yI x + xI = 3 + 8i + -6y + -1yI Reorder the terms: -3 + -8i + x + xI + 6y + yI = 3 + 8i + -6y + -1yI + -3 + -8i + 6y + yI Reorder the terms: -3 + -8i + x + xI + 6y + yI = 3 + -3 + 8i + -8i + -6y + 6y + -1yI + yI Combine like terms: 3 + -3 = 0 -3 + -8i + x + xI + 6y + yI = 0 + 8i + -8i + -6y + 6y + -1yI + yI -3 + -8i + x + xI + 6y + yI = 8i + -8i + -6y + 6y + -1yI + yI Combine like terms: 8i + -8i = 0 -3 + -8i + x + xI + 6y + yI = 0 + -6y + 6y + -1yI + yI -3 + -8i + x + xI + 6y + yI = -6y + 6y + -1yI + yI Combine like terms: -6y + 6y = 0 -3 + -8i + x + xI + 6y + yI = 0 + -1yI + yI -3 + -8i + x + xI + 6y + yI = -1yI + yI Combine like terms: -1yI + yI = 0 -3 + -8i + x + xI + 6y + yI = 0 The solution to this equation could not be determined.
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