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Simplifying (2m + n) + (m + -6n) * i = 7 + -1i Remove parenthesis around (2m + n) 2m + n + (m + -6n) * i = 7 + -1i Reorder the terms for easier multiplication: 2m + n + i(m + -6n) = 7 + -1i 2m + n + (m * i + -6n * i) = 7 + -1i 2m + n + (im + -6in) = 7 + -1i Reorder the terms: im + -6in + 2m + n = 7 + -1i Solving im + -6in + 2m + n = 7 + -1i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add 'i' to each side of the equation. im + -6in + 2m + i + n = 7 + -1i + i Reorder the terms: i + im + -6in + 2m + n = 7 + -1i + i Combine like terms: -1i + i = 0 i + im + -6in + 2m + n = 7 + 0 i + im + -6in + 2m + n = 7 Add '-2m' to each side of the equation. i + im + -6in + 2m + -2m + n = 7 + -2m Combine like terms: 2m + -2m = 0 i + im + -6in + 0 + n = 7 + -2m i + im + -6in + n = 7 + -2m Add '-1n' to each side of the equation. i + im + -6in + n + -1n = 7 + -2m + -1n Combine like terms: n + -1n = 0 i + im + -6in + 0 = 7 + -2m + -1n i + im + -6in = 7 + -2m + -1n Reorder the terms: -7 + i + im + -6in + 2m + n = 7 + -2m + -1n + -7 + 2m + n Reorder the terms: -7 + i + im + -6in + 2m + n = 7 + -7 + -2m + 2m + -1n + n Combine like terms: 7 + -7 = 0 -7 + i + im + -6in + 2m + n = 0 + -2m + 2m + -1n + n -7 + i + im + -6in + 2m + n = -2m + 2m + -1n + n Combine like terms: -2m + 2m = 0 -7 + i + im + -6in + 2m + n = 0 + -1n + n -7 + i + im + -6in + 2m + n = -1n + n Combine like terms: -1n + n = 0 -7 + i + im + -6in + 2m + n = 0 The solution to this equation could not be determined.
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