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Simplifying (m + 4n) + (2m + -3n) * i = 13 + 7i Remove parenthesis around (m + 4n) m + 4n + (2m + -3n) * i = 13 + 7i Reorder the terms for easier multiplication: m + 4n + i(2m + -3n) = 13 + 7i m + 4n + (2m * i + -3n * i) = 13 + 7i m + 4n + (2im + -3in) = 13 + 7i Reorder the terms: 2im + -3in + m + 4n = 13 + 7i Solving 2im + -3in + m + 4n = 13 + 7i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-7i' to each side of the equation. 2im + -3in + m + -7i + 4n = 13 + 7i + -7i Reorder the terms: -7i + 2im + -3in + m + 4n = 13 + 7i + -7i Combine like terms: 7i + -7i = 0 -7i + 2im + -3in + m + 4n = 13 + 0 -7i + 2im + -3in + m + 4n = 13 Add '-1m' to each side of the equation. -7i + 2im + -3in + m + -1m + 4n = 13 + -1m Combine like terms: m + -1m = 0 -7i + 2im + -3in + 0 + 4n = 13 + -1m -7i + 2im + -3in + 4n = 13 + -1m Add '-4n' to each side of the equation. -7i + 2im + -3in + 4n + -4n = 13 + -1m + -4n Combine like terms: 4n + -4n = 0 -7i + 2im + -3in + 0 = 13 + -1m + -4n -7i + 2im + -3in = 13 + -1m + -4n Reorder the terms: -13 + -7i + 2im + -3in + m + 4n = 13 + -1m + -4n + -13 + m + 4n Reorder the terms: -13 + -7i + 2im + -3in + m + 4n = 13 + -13 + -1m + m + -4n + 4n Combine like terms: 13 + -13 = 0 -13 + -7i + 2im + -3in + m + 4n = 0 + -1m + m + -4n + 4n -13 + -7i + 2im + -3in + m + 4n = -1m + m + -4n + 4n Combine like terms: -1m + m = 0 -13 + -7i + 2im + -3in + m + 4n = 0 + -4n + 4n -13 + -7i + 2im + -3in + m + 4n = -4n + 4n Combine like terms: -4n + 4n = 0 -13 + -7i + 2im + -3in + m + 4n = 0 The solution to this equation could not be determined.
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