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Simplifying (4 + i)(x + -1y) = 1 + -1i Multiply (4 + i) * (x + -1y) (4(x + -1y) + i(x + -1y)) = 1 + -1i ((x * 4 + -1y * 4) + i(x + -1y)) = 1 + -1i ((4x + -4y) + i(x + -1y)) = 1 + -1i (4x + -4y + (x * i + -1y * i)) = 1 + -1i (4x + -4y + (ix + -1iy)) = 1 + -1i Reorder the terms: (ix + -1iy + 4x + -4y) = 1 + -1i (ix + -1iy + 4x + -4y) = 1 + -1i Solving ix + -1iy + 4x + -4y = 1 + -1i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add 'i' to each side of the equation. ix + -1iy + 4x + i + -4y = 1 + -1i + i Reorder the terms: i + ix + -1iy + 4x + -4y = 1 + -1i + i Combine like terms: -1i + i = 0 i + ix + -1iy + 4x + -4y = 1 + 0 i + ix + -1iy + 4x + -4y = 1 Add '-4x' to each side of the equation. i + ix + -1iy + 4x + -4x + -4y = 1 + -4x Combine like terms: 4x + -4x = 0 i + ix + -1iy + 0 + -4y = 1 + -4x i + ix + -1iy + -4y = 1 + -4x Add '4y' to each side of the equation. i + ix + -1iy + -4y + 4y = 1 + -4x + 4y Combine like terms: -4y + 4y = 0 i + ix + -1iy + 0 = 1 + -4x + 4y i + ix + -1iy = 1 + -4x + 4y Reorder the terms: -1 + i + ix + -1iy + 4x + -4y = 1 + -4x + 4y + -1 + 4x + -4y Reorder the terms: -1 + i + ix + -1iy + 4x + -4y = 1 + -1 + -4x + 4x + 4y + -4y Combine like terms: 1 + -1 = 0 -1 + i + ix + -1iy + 4x + -4y = 0 + -4x + 4x + 4y + -4y -1 + i + ix + -1iy + 4x + -4y = -4x + 4x + 4y + -4y Combine like terms: -4x + 4x = 0 -1 + i + ix + -1iy + 4x + -4y = 0 + 4y + -4y -1 + i + ix + -1iy + 4x + -4y = 4y + -4y Combine like terms: 4y + -4y = 0 -1 + i + ix + -1iy + 4x + -4y = 0 The solution to this equation could not be determined.
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