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Simplifying 3z + 3i = 3(4i + -1) Reorder the terms: 3i + 3z = 3(4i + -1) Reorder the terms: 3i + 3z = 3(-1 + 4i) 3i + 3z = (-1 * 3 + 4i * 3) 3i + 3z = (-3 + 12i) Solving 3i + 3z = -3 + 12i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-12i' to each side of the equation. 3i + -12i + 3z = -3 + 12i + -12i Combine like terms: 3i + -12i = -9i -9i + 3z = -3 + 12i + -12i Combine like terms: 12i + -12i = 0 -9i + 3z = -3 + 0 -9i + 3z = -3 Add '-3z' to each side of the equation. -9i + 3z + -3z = -3 + -3z Combine like terms: 3z + -3z = 0 -9i + 0 = -3 + -3z -9i = -3 + -3z Divide each side by '-9'. i = 0.3333333333 + 0.3333333333z Simplifying i = 0.3333333333 + 0.3333333333z
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