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Simplifying (5 + -1i) * z = 2 + -1z Reorder the terms for easier multiplication: z(5 + -1i) = 2 + -1z (5 * z + -1i * z) = 2 + -1z Reorder the terms: (-1iz + 5z) = 2 + -1z (-1iz + 5z) = 2 + -1z Solving -1iz + 5z = 2 + -1z Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-5z' to each side of the equation. -1iz + 5z + -5z = 2 + -1z + -5z Combine like terms: 5z + -5z = 0 -1iz + 0 = 2 + -1z + -5z -1iz = 2 + -1z + -5z Combine like terms: -1z + -5z = -6z -1iz = 2 + -6z Divide each side by '-1z'. i = -2z-1 + 6 Simplifying i = -2z-1 + 6 Reorder the terms: i = 6 + -2z-1
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