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Simplifying (-8 + -9i) + -1(2 + 7i) + (-9 + -9i) = 0 Remove parenthesis around (-8 + -9i) -8 + -9i + -1(2 + 7i) + (-9 + -9i) = 0 -8 + -9i + (2 * -1 + 7i * -1) + (-9 + -9i) = 0 -8 + -9i + (-2 + -7i) + (-9 + -9i) = 0 Remove parenthesis around (-9 + -9i) -8 + -9i + -2 + -7i + -9 + -9i = 0 Reorder the terms: -8 + -2 + -9 + -9i + -7i + -9i = 0 Combine like terms: -8 + -2 = -10 -10 + -9 + -9i + -7i + -9i = 0 Combine like terms: -10 + -9 = -19 -19 + -9i + -7i + -9i = 0 Combine like terms: -9i + -7i = -16i -19 + -16i + -9i = 0 Combine like terms: -16i + -9i = -25i -19 + -25i = 0 Solving -19 + -25i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + -25i = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -25i = 0 + 19 -25i = 0 + 19 Combine like terms: 0 + 19 = 19 -25i = 19 Divide each side by '-25'. i = -0.76 Simplifying i = -0.76
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