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Simplifying 6 + -1(-4 + 9i) + -1(-1 + -1i) = 0 6 + (-4 * -1 + 9i * -1) + -1(-1 + -1i) = 0 6 + (4 + -9i) + -1(-1 + -1i) = 0 6 + 4 + -9i + (-1 * -1 + -1i * -1) = 0 6 + 4 + -9i + (1 + 1i) = 0 Reorder the terms: 6 + 4 + 1 + -9i + 1i = 0 Combine like terms: 6 + 4 = 10 10 + 1 + -9i + 1i = 0 Combine like terms: 10 + 1 = 11 11 + -9i + 1i = 0 Combine like terms: -9i + 1i = -8i 11 + -8i = 0 Solving 11 + -8i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -8i = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -8i = 0 + -11 -8i = 0 + -11 Combine like terms: 0 + -11 = -11 -8i = -11 Divide each side by '-8'. i = 1.375 Simplifying i = 1.375
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