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Simplifying z4 + 4z3 + 6z2 + 4z + 1 + i = 0 Reorder the terms: 1 + i + 4z + 6z2 + 4z3 + z4 = 0 Solving 1 + i + 4z + 6z2 + 4z3 + z4 = 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 + i + 4z + 6z2 + 4z3 + -1 + z4 = 0 + -1 Reorder the terms: 1 + -1 + i + 4z + 6z2 + 4z3 + z4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + i + 4z + 6z2 + 4z3 + z4 = 0 + -1 i + 4z + 6z2 + 4z3 + z4 = 0 + -1 Combine like terms: 0 + -1 = -1 i + 4z + 6z2 + 4z3 + z4 = -1 Add '-4z' to each side of the equation. i + 4z + 6z2 + 4z3 + -4z + z4 = -1 + -4z Reorder the terms: i + 4z + -4z + 6z2 + 4z3 + z4 = -1 + -4z Combine like terms: 4z + -4z = 0 i + 0 + 6z2 + 4z3 + z4 = -1 + -4z i + 6z2 + 4z3 + z4 = -1 + -4z Add '-6z2' to each side of the equation. i + 6z2 + 4z3 + -6z2 + z4 = -1 + -4z + -6z2 Reorder the terms: i + 6z2 + -6z2 + 4z3 + z4 = -1 + -4z + -6z2 Combine like terms: 6z2 + -6z2 = 0 i + 0 + 4z3 + z4 = -1 + -4z + -6z2 i + 4z3 + z4 = -1 + -4z + -6z2 Add '-4z3' to each side of the equation. i + 4z3 + -4z3 + z4 = -1 + -4z + -6z2 + -4z3 Combine like terms: 4z3 + -4z3 = 0 i + 0 + z4 = -1 + -4z + -6z2 + -4z3 i + z4 = -1 + -4z + -6z2 + -4z3 Add '-1z4' to each side of the equation. i + z4 + -1z4 = -1 + -4z + -6z2 + -4z3 + -1z4 Combine like terms: z4 + -1z4 = 0 i + 0 = -1 + -4z + -6z2 + -4z3 + -1z4 i = -1 + -4z + -6z2 + -4z3 + -1z4 Simplifying i = -1 + -4z + -6z2 + -4z3 + -1z4
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