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Simplifying (x + -2y)(3 + 5i) = 7 + -3i Multiply (x + -2y) * (3 + 5i) (x(3 + 5i) + -2y * (3 + 5i)) = 7 + -3i ((3 * x + 5i * x) + -2y * (3 + 5i)) = 7 + -3i Reorder the terms: ((5ix + 3x) + -2y * (3 + 5i)) = 7 + -3i ((5ix + 3x) + -2y * (3 + 5i)) = 7 + -3i (5ix + 3x + (3 * -2y + 5i * -2y)) = 7 + -3i Reorder the terms: (5ix + 3x + (-10iy + -6y)) = 7 + -3i (5ix + 3x + (-10iy + -6y)) = 7 + -3i Reorder the terms: (5ix + -10iy + 3x + -6y) = 7 + -3i (5ix + -10iy + 3x + -6y) = 7 + -3i Solving 5ix + -10iy + 3x + -6y = 7 + -3i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '3i' to each side of the equation. 5ix + -10iy + 3x + 3i + -6y = 7 + -3i + 3i Reorder the terms: 3i + 5ix + -10iy + 3x + -6y = 7 + -3i + 3i Combine like terms: -3i + 3i = 0 3i + 5ix + -10iy + 3x + -6y = 7 + 0 3i + 5ix + -10iy + 3x + -6y = 7 Add '-3x' to each side of the equation. 3i + 5ix + -10iy + 3x + -3x + -6y = 7 + -3x Combine like terms: 3x + -3x = 0 3i + 5ix + -10iy + 0 + -6y = 7 + -3x 3i + 5ix + -10iy + -6y = 7 + -3x Add '6y' to each side of the equation. 3i + 5ix + -10iy + -6y + 6y = 7 + -3x + 6y Combine like terms: -6y + 6y = 0 3i + 5ix + -10iy + 0 = 7 + -3x + 6y 3i + 5ix + -10iy = 7 + -3x + 6y Reorder the terms: -7 + 3i + 5ix + -10iy + 3x + -6y = 7 + -3x + 6y + -7 + 3x + -6y Reorder the terms: -7 + 3i + 5ix + -10iy + 3x + -6y = 7 + -7 + -3x + 3x + 6y + -6y Combine like terms: 7 + -7 = 0 -7 + 3i + 5ix + -10iy + 3x + -6y = 0 + -3x + 3x + 6y + -6y -7 + 3i + 5ix + -10iy + 3x + -6y = -3x + 3x + 6y + -6y Combine like terms: -3x + 3x = 0 -7 + 3i + 5ix + -10iy + 3x + -6y = 0 + 6y + -6y -7 + 3i + 5ix + -10iy + 3x + -6y = 6y + -6y Combine like terms: 6y + -6y = 0 -7 + 3i + 5ix + -10iy + 3x + -6y = 0 The solution to this equation could not be determined.
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