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Simplifying (m + 2n) + (2m + -1n) * i = 5 + 5i Remove parenthesis around (m + 2n) m + 2n + (2m + -1n) * i = 5 + 5i Reorder the terms for easier multiplication: m + 2n + i(2m + -1n) = 5 + 5i m + 2n + (2m * i + -1n * i) = 5 + 5i m + 2n + (2im + -1in) = 5 + 5i Reorder the terms: 2im + -1in + m + 2n = 5 + 5i Solving 2im + -1in + m + 2n = 5 + 5i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-5i' to each side of the equation. 2im + -1in + m + -5i + 2n = 5 + 5i + -5i Reorder the terms: -5i + 2im + -1in + m + 2n = 5 + 5i + -5i Combine like terms: 5i + -5i = 0 -5i + 2im + -1in + m + 2n = 5 + 0 -5i + 2im + -1in + m + 2n = 5 Add '-1m' to each side of the equation. -5i + 2im + -1in + m + -1m + 2n = 5 + -1m Combine like terms: m + -1m = 0 -5i + 2im + -1in + 0 + 2n = 5 + -1m -5i + 2im + -1in + 2n = 5 + -1m Add '-2n' to each side of the equation. -5i + 2im + -1in + 2n + -2n = 5 + -1m + -2n Combine like terms: 2n + -2n = 0 -5i + 2im + -1in + 0 = 5 + -1m + -2n -5i + 2im + -1in = 5 + -1m + -2n Reorder the terms: -5 + -5i + 2im + -1in + m + 2n = 5 + -1m + -2n + -5 + m + 2n Reorder the terms: -5 + -5i + 2im + -1in + m + 2n = 5 + -5 + -1m + m + -2n + 2n Combine like terms: 5 + -5 = 0 -5 + -5i + 2im + -1in + m + 2n = 0 + -1m + m + -2n + 2n -5 + -5i + 2im + -1in + m + 2n = -1m + m + -2n + 2n Combine like terms: -1m + m = 0 -5 + -5i + 2im + -1in + m + 2n = 0 + -2n + 2n -5 + -5i + 2im + -1in + m + 2n = -2n + 2n Combine like terms: -2n + 2n = 0 -5 + -5i + 2im + -1in + m + 2n = 0 The solution to this equation could not be determined.
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