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Simplifying 3z + 12 + -5i = 0 Reorder the terms: 12 + -5i + 3z = 0 Solving 12 + -5i + 3z = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -5i + -12 + 3z = 0 + -12 Reorder the terms: 12 + -12 + -5i + 3z = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -5i + 3z = 0 + -12 -5i + 3z = 0 + -12 Combine like terms: 0 + -12 = -12 -5i + 3z = -12 Add '-3z' to each side of the equation. -5i + 3z + -3z = -12 + -3z Combine like terms: 3z + -3z = 0 -5i + 0 = -12 + -3z -5i = -12 + -3z Divide each side by '-5'. i = 2.4 + 0.6z Simplifying i = 2.4 + 0.6z
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