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Simplifying z + (-1 + 7i) = -4 + -5i Remove parenthesis around (-1 + 7i) z + -1 + 7i = -4 + -5i Reorder the terms: -1 + 7i + z = -4 + -5i Solving -1 + 7i + z = -4 + -5i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '5i' to each side of the equation. -1 + 7i + 5i + z = -4 + -5i + 5i Combine like terms: 7i + 5i = 12i -1 + 12i + z = -4 + -5i + 5i Combine like terms: -5i + 5i = 0 -1 + 12i + z = -4 + 0 -1 + 12i + z = -4 Add '1' to each side of the equation. -1 + 12i + 1 + z = -4 + 1 Reorder the terms: -1 + 1 + 12i + z = -4 + 1 Combine like terms: -1 + 1 = 0 0 + 12i + z = -4 + 1 12i + z = -4 + 1 Combine like terms: -4 + 1 = -3 12i + z = -3 Add '-1z' to each side of the equation. 12i + z + -1z = -3 + -1z Combine like terms: z + -1z = 0 12i + 0 = -3 + -1z 12i = -3 + -1z Divide each side by '12'. i = -0.25 + -0.08333333333z Simplifying i = -0.25 + -0.08333333333z
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