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Simplifying (4 + 5i)(4 + 1) = 0 Combine like terms: 4 + 1 = 5 (4 + 5i)(5) = 0 Reorder the terms for easier multiplication: 5(4 + 5i) = 0 (4 * 5 + 5i * 5) = 0 (20 + 25i) = 0 Solving 20 + 25i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + 25i = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 25i = 0 + -20 25i = 0 + -20 Combine like terms: 0 + -20 = -20 25i = -20 Divide each side by '25'. i = -0.8 Simplifying i = -0.8
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