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Simplifying z2 + 4Z + (4 + 2i) = 0 Remove parenthesis around (4 + 2i) z2 + 4Z + 4 + 2i = 0 Reorder the terms: 4 + 4Z + 2i + z2 = 0 Solving 4 + 4Z + 2i + z2 = 0 Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + 4Z + 2i + -4 + z2 = 0 + -4 Reorder the terms: 4 + -4 + 4Z + 2i + z2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 4Z + 2i + z2 = 0 + -4 4Z + 2i + z2 = 0 + -4 Combine like terms: 0 + -4 = -4 4Z + 2i + z2 = -4 Add '-2i' to each side of the equation. 4Z + 2i + -2i + z2 = -4 + -2i Combine like terms: 2i + -2i = 0 4Z + 0 + z2 = -4 + -2i 4Z + z2 = -4 + -2i Add '-1z2' to each side of the equation. 4Z + z2 + -1z2 = -4 + -2i + -1z2 Combine like terms: z2 + -1z2 = 0 4Z + 0 = -4 + -2i + -1z2 4Z = -4 + -2i + -1z2 Divide each side by '4'. Z = -1 + -0.5i + -0.25z2 Simplifying Z = -1 + -0.5i + -0.25z2
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