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Simplifying 4z + 2i = 6 + -7i + z Reorder the terms: 2i + 4z = 6 + -7i + z Solving 2i + 4z = 6 + -7i + z 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. 2i + 7i + 4z = 6 + -7i + 7i + z Combine like terms: 2i + 7i = 9i 9i + 4z = 6 + -7i + 7i + z Combine like terms: -7i + 7i = 0 9i + 4z = 6 + 0 + z 9i + 4z = 6 + z Add '-4z' to each side of the equation. 9i + 4z + -4z = 6 + z + -4z Combine like terms: 4z + -4z = 0 9i + 0 = 6 + z + -4z 9i = 6 + z + -4z Combine like terms: z + -4z = -3z 9i = 6 + -3z Divide each side by '9'. i = 0.6666666667 + -0.3333333333z Simplifying i = 0.6666666667 + -0.3333333333z
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