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Simplifying (3 + 2i) * x = 0 Reorder the terms for easier multiplication: x(3 + 2i) = 0 (3 * x + 2i * x) = 0 Reorder the terms: (2ix + 3x) = 0 (2ix + 3x) = 0 Solving 2ix + 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. 2ix + 3x + -3x = 0 + -3x Combine like terms: 3x + -3x = 0 2ix + 0 = 0 + -3x 2ix = 0 + -3x Remove the zero: 2ix = -3x Divide each side by '2x'. i = -1.5 Simplifying i = -1.5
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