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Simplifying z(1 + 3i) = 0 (1 * z + 3i * z) = 0 Reorder the terms: (3iz + 1z) = 0 (3iz + 1z) = 0 Solving 3iz + 1z = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1z' to each side of the equation. 3iz + 1z + -1z = 0 + -1z Combine like terms: 1z + -1z = 0 3iz + 0 = 0 + -1z 3iz = 0 + -1z Remove the zero: 3iz = -1z Divide each side by '3z'. i = -0.3333333333 Simplifying i = -0.3333333333
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