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