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