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