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Simplifying (4 + -9i) + -1(2 + 3i) = 0 Remove parenthesis around (4 + -9i) 4 + -9i + -1(2 + 3i) = 0 4 + -9i + (2 * -1 + 3i * -1) = 0 4 + -9i + (-2 + -3i) = 0 Reorder the terms: 4 + -2 + -9i + -3i = 0 Combine like terms: 4 + -2 = 2 2 + -9i + -3i = 0 Combine like terms: -9i + -3i = -12i 2 + -12i = 0 Solving 2 + -12i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -12i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -12i = 0 + -2 -12i = 0 + -2 Combine like terms: 0 + -2 = -2 -12i = -2 Divide each side by '-12'. i = 0.1666666667 Simplifying i = 0.1666666667
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