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Simplifying (-2 + -2i) * z = z + 6 Reorder the terms for easier multiplication: z(-2 + -2i) = z + 6 (-2 * z + -2i * z) = z + 6 Reorder the terms: (-2iz + -2z) = z + 6 (-2iz + -2z) = z + 6 Reorder the terms: -2iz + -2z = 6 + z Solving -2iz + -2z = 6 + z Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '2z' to each side of the equation. -2iz + -2z + 2z = 6 + z + 2z Combine like terms: -2z + 2z = 0 -2iz + 0 = 6 + z + 2z -2iz = 6 + z + 2z Combine like terms: z + 2z = 3z -2iz = 6 + 3z Divide each side by '-2z'. i = -3z-1 + -1.5 Simplifying i = -3z-1 + -1.5 Reorder the terms: i = -1.5 + -3z-1
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