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Simplifying 3 + -1(-6 + -9i) + -1(-7 + 2i) = 0 3 + (-6 * -1 + -9i * -1) + -1(-7 + 2i) = 0 3 + (6 + 9i) + -1(-7 + 2i) = 0 3 + 6 + 9i + (-7 * -1 + 2i * -1) = 0 3 + 6 + 9i + (7 + -2i) = 0 Reorder the terms: 3 + 6 + 7 + 9i + -2i = 0 Combine like terms: 3 + 6 = 9 9 + 7 + 9i + -2i = 0 Combine like terms: 9 + 7 = 16 16 + 9i + -2i = 0 Combine like terms: 9i + -2i = 7i 16 + 7i = 0 Solving 16 + 7i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + 7i = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 7i = 0 + -16 7i = 0 + -16 Combine like terms: 0 + -16 = -16 7i = -16 Divide each side by '7'. i = -2.285714286 Simplifying i = -2.285714286
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