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Simplifying (1 + 3i) * x + 4 = 3 + -2i Reorder the terms for easier multiplication: x(1 + 3i) + 4 = 3 + -2i (1 * x + 3i * x) + 4 = 3 + -2i Reorder the terms: (3ix + 1x) + 4 = 3 + -2i (3ix + 1x) + 4 = 3 + -2i Reorder the terms: 4 + 3ix + 1x = 3 + -2i Solving 4 + 3ix + 1x = 3 + -2i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '2i' to each side of the equation. 4 + 3ix + 2i + 1x = 3 + -2i + 2i Reorder the terms: 4 + 2i + 3ix + 1x = 3 + -2i + 2i Combine like terms: -2i + 2i = 0 4 + 2i + 3ix + 1x = 3 + 0 4 + 2i + 3ix + 1x = 3 Add '-4' to each side of the equation. 4 + 2i + 3ix + -4 + 1x = 3 + -4 Reorder the terms: 4 + -4 + 2i + 3ix + 1x = 3 + -4 Combine like terms: 4 + -4 = 0 0 + 2i + 3ix + 1x = 3 + -4 2i + 3ix + 1x = 3 + -4 Combine like terms: 3 + -4 = -1 2i + 3ix + 1x = -1 Add '-1x' to each side of the equation. 2i + 3ix + 1x + -1x = -1 + -1x Combine like terms: 1x + -1x = 0 2i + 3ix + 0 = -1 + -1x 2i + 3ix = -1 + -1x Reorder the terms: 1 + 2i + 3ix + x = -1 + -1x + 1 + x Reorder the terms: 1 + 2i + 3ix + x = -1 + 1 + -1x + x Combine like terms: -1 + 1 = 0 1 + 2i + 3ix + x = 0 + -1x + x 1 + 2i + 3ix + x = -1x + x Combine like terms: -1x + x = 0 1 + 2i + 3ix + x = 0 The solution to this equation could not be determined.
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