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Simplifying (10 + -2i) * z + (5 + i) = 2i Reorder the terms for easier multiplication: z(10 + -2i) + (5 + i) = 2i (10 * z + -2i * z) + (5 + i) = 2i Reorder the terms: (-2iz + 10z) + (5 + i) = 2i (-2iz + 10z) + (5 + i) = 2i Remove parenthesis around (5 + i) -2iz + 10z + 5 + i = 2i Reorder the terms: 5 + i + -2iz + 10z = 2i Solving 5 + i + -2iz + 10z = 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. 5 + i + -2iz + -2i + 10z = 2i + -2i Reorder the terms: 5 + i + -2i + -2iz + 10z = 2i + -2i Combine like terms: i + -2i = -1i 5 + -1i + -2iz + 10z = 2i + -2i Combine like terms: 2i + -2i = 0 5 + -1i + -2iz + 10z = 0 Add '-5' to each side of the equation. 5 + -1i + -2iz + -5 + 10z = 0 + -5 Reorder the terms: 5 + -5 + -1i + -2iz + 10z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1i + -2iz + 10z = 0 + -5 -1i + -2iz + 10z = 0 + -5 Combine like terms: 0 + -5 = -5 -1i + -2iz + 10z = -5 Add '-10z' to each side of the equation. -1i + -2iz + 10z + -10z = -5 + -10z Combine like terms: 10z + -10z = 0 -1i + -2iz + 0 = -5 + -10z -1i + -2iz = -5 + -10z Reorder the terms: 5 + -1i + -2iz + 10z = -5 + -10z + 5 + 10z Reorder the terms: 5 + -1i + -2iz + 10z = -5 + 5 + -10z + 10z Combine like terms: -5 + 5 = 0 5 + -1i + -2iz + 10z = 0 + -10z + 10z 5 + -1i + -2iz + 10z = -10z + 10z Combine like terms: -10z + 10z = 0 5 + -1i + -2iz + 10z = 0 The solution to this equation could not be determined.
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