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Simplifying z + (-2 + 9i) = -5 + -7i Remove parenthesis around (-2 + 9i) z + -2 + 9i = -5 + -7i Reorder the terms: -2 + 9i + z = -5 + -7i Solving -2 + 9i + z = -5 + -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. -2 + 9i + 7i + z = -5 + -7i + 7i Combine like terms: 9i + 7i = 16i -2 + 16i + z = -5 + -7i + 7i Combine like terms: -7i + 7i = 0 -2 + 16i + z = -5 + 0 -2 + 16i + z = -5 Add '2' to each side of the equation. -2 + 16i + 2 + z = -5 + 2 Reorder the terms: -2 + 2 + 16i + z = -5 + 2 Combine like terms: -2 + 2 = 0 0 + 16i + z = -5 + 2 16i + z = -5 + 2 Combine like terms: -5 + 2 = -3 16i + z = -3 Add '-1z' to each side of the equation. 16i + z + -1z = -3 + -1z Combine like terms: z + -1z = 0 16i + 0 = -3 + -1z 16i = -3 + -1z Divide each side by '16'. i = -0.1875 + -0.0625z Simplifying i = -0.1875 + -0.0625z
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