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Simplifying z + -2z + 7 + 6i = 0 Reorder the terms: 7 + 6i + z + -2z = 0 Combine like terms: z + -2z = -1z 7 + 6i + -1z = 0 Solving 7 + 6i + -1z = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + 6i + -7 + -1z = 0 + -7 Reorder the terms: 7 + -7 + 6i + -1z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6i + -1z = 0 + -7 6i + -1z = 0 + -7 Combine like terms: 0 + -7 = -7 6i + -1z = -7 Add 'z' to each side of the equation. 6i + -1z + z = -7 + z Combine like terms: -1z + z = 0 6i + 0 = -7 + z 6i = -7 + z Divide each side by '6'. i = -1.166666667 + 0.1666666667z Simplifying i = -1.166666667 + 0.1666666667z
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