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Simplifying (-9 + 2i) + -1(2 + 9i) = 0 Remove parenthesis around (-9 + 2i) -9 + 2i + -1(2 + 9i) = 0 -9 + 2i + (2 * -1 + 9i * -1) = 0 -9 + 2i + (-2 + -9i) = 0 Reorder the terms: -9 + -2 + 2i + -9i = 0 Combine like terms: -9 + -2 = -11 -11 + 2i + -9i = 0 Combine like terms: 2i + -9i = -7i -11 + -7i = 0 Solving -11 + -7i = 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 + -7i = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -7i = 0 + 11 -7i = 0 + 11 Combine like terms: 0 + 11 = 11 -7i = 11 Divide each side by '-7'. i = -1.571428571 Simplifying i = -1.571428571
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