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Simplifying z + 2z + 7 + -6i = 0 Reorder the terms: 7 + -6i + z + 2z = 0 Combine like terms: z + 2z = 3z 7 + -6i + 3z = 0 Solving 7 + -6i + 3z = 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 + 3z = 0 + -7 Reorder the terms: 7 + -7 + -6i + 3z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6i + 3z = 0 + -7 -6i + 3z = 0 + -7 Combine like terms: 0 + -7 = -7 -6i + 3z = -7 Add '-3z' to each side of the equation. -6i + 3z + -3z = -7 + -3z Combine like terms: 3z + -3z = 0 -6i + 0 = -7 + -3z -6i = -7 + -3z Divide each side by '-6'. i = 1.166666667 + 0.5z Simplifying i = 1.166666667 + 0.5z
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