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Simplifying (10m + -9n) + (5m + -4n) * i = 15 + 10i Remove parenthesis around (10m + -9n) 10m + -9n + (5m + -4n) * i = 15 + 10i Reorder the terms for easier multiplication: 10m + -9n + i(5m + -4n) = 15 + 10i 10m + -9n + (5m * i + -4n * i) = 15 + 10i 10m + -9n + (5im + -4in) = 15 + 10i Reorder the terms: 5im + -4in + 10m + -9n = 15 + 10i Solving 5im + -4in + 10m + -9n = 15 + 10i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-10i' to each side of the equation. 5im + -4in + 10m + -10i + -9n = 15 + 10i + -10i Reorder the terms: -10i + 5im + -4in + 10m + -9n = 15 + 10i + -10i Combine like terms: 10i + -10i = 0 -10i + 5im + -4in + 10m + -9n = 15 + 0 -10i + 5im + -4in + 10m + -9n = 15 Add '-10m' to each side of the equation. -10i + 5im + -4in + 10m + -10m + -9n = 15 + -10m Combine like terms: 10m + -10m = 0 -10i + 5im + -4in + 0 + -9n = 15 + -10m -10i + 5im + -4in + -9n = 15 + -10m Add '9n' to each side of the equation. -10i + 5im + -4in + -9n + 9n = 15 + -10m + 9n Combine like terms: -9n + 9n = 0 -10i + 5im + -4in + 0 = 15 + -10m + 9n -10i + 5im + -4in = 15 + -10m + 9n Reorder the terms: -15 + -10i + 5im + -4in + 10m + -9n = 15 + -10m + 9n + -15 + 10m + -9n Reorder the terms: -15 + -10i + 5im + -4in + 10m + -9n = 15 + -15 + -10m + 10m + 9n + -9n Combine like terms: 15 + -15 = 0 -15 + -10i + 5im + -4in + 10m + -9n = 0 + -10m + 10m + 9n + -9n -15 + -10i + 5im + -4in + 10m + -9n = -10m + 10m + 9n + -9n Combine like terms: -10m + 10m = 0 -15 + -10i + 5im + -4in + 10m + -9n = 0 + 9n + -9n -15 + -10i + 5im + -4in + 10m + -9n = 9n + -9n Combine like terms: 9n + -9n = 0 -15 + -10i + 5im + -4in + 10m + -9n = 0 The solution to this equation could not be determined.
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