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Simplifying 6(-5 + 4i) + -1(-13 + -1i) = 0 (-5 * 6 + 4i * 6) + -1(-13 + -1i) = 0 (-30 + 24i) + -1(-13 + -1i) = 0 -30 + 24i + (-13 * -1 + -1i * -1) = 0 -30 + 24i + (13 + 1i) = 0 Reorder the terms: -30 + 13 + 24i + 1i = 0 Combine like terms: -30 + 13 = -17 -17 + 24i + 1i = 0 Combine like terms: 24i + 1i = 25i -17 + 25i = 0 Solving -17 + 25i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + 25i = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 25i = 0 + 17 25i = 0 + 17 Combine like terms: 0 + 17 = 17 25i = 17 Divide each side by '25'. i = 0.68 Simplifying i = 0.68
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