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Simplifying (4 + -3i)(7 + 1) = 0 Combine like terms: 7 + 1 = 8 (4 + -3i)(8) = 0 Reorder the terms for easier multiplication: 8(4 + -3i) = 0 (4 * 8 + -3i * 8) = 0 (32 + -24i) = 0 Solving 32 + -24i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + -24i = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -24i = 0 + -32 -24i = 0 + -32 Combine like terms: 0 + -32 = -32 -24i = -32 Divide each side by '-24'. i = 1.333333333 Simplifying i = 1.333333333
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