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