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Simplifying 2 + i + 3Z = Z + -1i Reorder the terms: 2 + 3Z + i = Z + -1i Solving 2 + 3Z + i = Z + -1i Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '-1Z' to each side of the equation. 2 + 3Z + -1Z + i = Z + -1Z + -1i Combine like terms: 3Z + -1Z = 2Z 2 + 2Z + i = Z + -1Z + -1i Combine like terms: Z + -1Z = 0 2 + 2Z + i = 0 + -1i 2 + 2Z + i = -1i Add '-2' to each side of the equation. 2 + 2Z + -2 + i = -2 + -1i Reorder the terms: 2 + -2 + 2Z + i = -2 + -1i Combine like terms: 2 + -2 = 0 0 + 2Z + i = -2 + -1i 2Z + i = -2 + -1i Add '-1i' to each side of the equation. 2Z + i + -1i = -2 + -1i + -1i Combine like terms: i + -1i = 0 2Z + 0 = -2 + -1i + -1i 2Z = -2 + -1i + -1i Combine like terms: -1i + -1i = -2i 2Z = -2 + -2i Divide each side by '2'. Z = -1 + -1i Simplifying Z = -1 + -1i
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