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Simplifying z2 + 4z + -1 + 12i = 0 Reorder the terms: -1 + 12i + 4z + z2 = 0 Solving -1 + 12i + 4z + z2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 12i + 4z + 1 + z2 = 0 + 1 Reorder the terms: -1 + 1 + 12i + 4z + z2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 12i + 4z + z2 = 0 + 1 12i + 4z + z2 = 0 + 1 Combine like terms: 0 + 1 = 1 12i + 4z + z2 = 1 Add '-4z' to each side of the equation. 12i + 4z + -4z + z2 = 1 + -4z Combine like terms: 4z + -4z = 0 12i + 0 + z2 = 1 + -4z 12i + z2 = 1 + -4z Add '-1z2' to each side of the equation. 12i + z2 + -1z2 = 1 + -4z + -1z2 Combine like terms: z2 + -1z2 = 0 12i + 0 = 1 + -4z + -1z2 12i = 1 + -4z + -1z2 Divide each side by '12'. i = 0.08333333333 + -0.3333333333z + -0.08333333333z2 Simplifying i = 0.08333333333 + -0.3333333333z + -0.08333333333z2
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