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Simplifying (5 + i) * x + -1(2 + -3i) * x = 0 Reorder the terms for easier multiplication: x(5 + i) + -1(2 + -3i) * x = 0 (5 * x + i * x) + -1(2 + -3i) * x = 0 Reorder the terms: (ix + 5x) + -1(2 + -3i) * x = 0 (ix + 5x) + -1(2 + -3i) * x = 0 Reorder the terms for easier multiplication: ix + 5x + -1x(2 + -3i) = 0 ix + 5x + (2 * -1x + -3i * -1x) = 0 Reorder the terms: ix + 5x + (3ix + -2x) = 0 ix + 5x + (3ix + -2x) = 0 Reorder the terms: ix + 3ix + 5x + -2x = 0 Combine like terms: ix + 3ix = 4ix 4ix + 5x + -2x = 0 Combine like terms: 5x + -2x = 3x 4ix + 3x = 0 Solving 4ix + 3x = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3x' to each side of the equation. 4ix + 3x + -3x = 0 + -3x Combine like terms: 3x + -3x = 0 4ix + 0 = 0 + -3x 4ix = 0 + -3x Remove the zero: 4ix = -3x Divide each side by '4x'. i = -0.75 Simplifying i = -0.75
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