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Simplifying 2m + -3n + (m + 4n) * i = 13 + 7i Reorder the terms for easier multiplication: 2m + -3n + i(m + 4n) = 13 + 7i 2m + -3n + (m * i + 4n * i) = 13 + 7i 2m + -3n + (im + 4in) = 13 + 7i Reorder the terms: im + 4in + 2m + -3n = 13 + 7i Solving im + 4in + 2m + -3n = 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. im + 4in + 2m + -7i + -3n = 13 + 7i + -7i Reorder the terms: -7i + im + 4in + 2m + -3n = 13 + 7i + -7i Combine like terms: 7i + -7i = 0 -7i + im + 4in + 2m + -3n = 13 + 0 -7i + im + 4in + 2m + -3n = 13 Add '-2m' to each side of the equation. -7i + im + 4in + 2m + -2m + -3n = 13 + -2m Combine like terms: 2m + -2m = 0 -7i + im + 4in + 0 + -3n = 13 + -2m -7i + im + 4in + -3n = 13 + -2m Add '3n' to each side of the equation. -7i + im + 4in + -3n + 3n = 13 + -2m + 3n Combine like terms: -3n + 3n = 0 -7i + im + 4in + 0 = 13 + -2m + 3n -7i + im + 4in = 13 + -2m + 3n Reorder the terms: -13 + -7i + im + 4in + 2m + -3n = 13 + -2m + 3n + -13 + 2m + -3n Reorder the terms: -13 + -7i + im + 4in + 2m + -3n = 13 + -13 + -2m + 2m + 3n + -3n Combine like terms: 13 + -13 = 0 -13 + -7i + im + 4in + 2m + -3n = 0 + -2m + 2m + 3n + -3n -13 + -7i + im + 4in + 2m + -3n = -2m + 2m + 3n + -3n Combine like terms: -2m + 2m = 0 -13 + -7i + im + 4in + 2m + -3n = 0 + 3n + -3n -13 + -7i + im + 4in + 2m + -3n = 3n + -3n Combine like terms: 3n + -3n = 0 -13 + -7i + im + 4in + 2m + -3n = 0 The solution to this equation could not be determined.
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