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Simplifying 4z2 + 4z + 1 + -4i = 0 Reorder the terms: 1 + -4i + 4z + 4z2 = 0 Solving 1 + -4i + 4z + 4z2 = 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 + -4i + 4z + -1 + 4z2 = 0 + -1 Reorder the terms: 1 + -1 + -4i + 4z + 4z2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4i + 4z + 4z2 = 0 + -1 -4i + 4z + 4z2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4i + 4z + 4z2 = -1 Add '-4z' to each side of the equation. -4i + 4z + -4z + 4z2 = -1 + -4z Combine like terms: 4z + -4z = 0 -4i + 0 + 4z2 = -1 + -4z -4i + 4z2 = -1 + -4z Add '-4z2' to each side of the equation. -4i + 4z2 + -4z2 = -1 + -4z + -4z2 Combine like terms: 4z2 + -4z2 = 0 -4i + 0 = -1 + -4z + -4z2 -4i = -1 + -4z + -4z2 Divide each side by '-4'. i = 0.25 + z + z2 Simplifying i = 0.25 + z + z2
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