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Simplifying 3z + 4i = 3 + -2i Reorder the terms: 4i + 3z = 3 + -2i Solving 4i + 3z = 3 + -2i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '2i' to each side of the equation. 4i + 2i + 3z = 3 + -2i + 2i Combine like terms: 4i + 2i = 6i 6i + 3z = 3 + -2i + 2i Combine like terms: -2i + 2i = 0 6i + 3z = 3 + 0 6i + 3z = 3 Add '-3z' to each side of the equation. 6i + 3z + -3z = 3 + -3z Combine like terms: 3z + -3z = 0 6i + 0 = 3 + -3z 6i = 3 + -3z Divide each side by '6'. i = 0.5 + -0.5z Simplifying i = 0.5 + -0.5z
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