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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 = 43 43 + -24i + 1i = 0 Combine like terms: -24i + 1i = -23i 43 + -23i = 0 Solving 43 + -23i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-43' to each side of the equation. 43 + -43 + -23i = 0 + -43 Combine like terms: 43 + -43 = 0 0 + -23i = 0 + -43 -23i = 0 + -43 Combine like terms: 0 + -43 = -43 -23i = -43 Divide each side by '-23'. i = 1.869565217 Simplifying i = 1.869565217
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