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Simplifying 3i(-1 + 9) + -4(-6 + -5i) = 0 Combine like terms: -1 + 9 = 8 3i(8) + -4(-6 + -5i) = 0 Reorder the terms for easier multiplication: 3 * 8i + -4(-6 + -5i) = 0 Multiply 3 * 8 24i + -4(-6 + -5i) = 0 24i + (-6 * -4 + -5i * -4) = 0 24i + (24 + 20i) = 0 Reorder the terms: 24 + 24i + 20i = 0 Combine like terms: 24i + 20i = 44i 24 + 44i = 0 Solving 24 + 44i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + 44i = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 44i = 0 + -24 44i = 0 + -24 Combine like terms: 0 + -24 = -24 44i = -24 Divide each side by '44'. i = -0.5454545455 Simplifying i = -0.5454545455
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