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Simplifying 2m + 3n + 1i = 6 + -8i Reorder the terms: 1i + 2m + 3n = 6 + -8i Solving 1i + 2m + 3n = 6 + -8i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '8i' to each side of the equation. 1i + 2m + 8i + 3n = 6 + -8i + 8i Reorder the terms: 1i + 8i + 2m + 3n = 6 + -8i + 8i Combine like terms: 1i + 8i = 9i 9i + 2m + 3n = 6 + -8i + 8i Combine like terms: -8i + 8i = 0 9i + 2m + 3n = 6 + 0 9i + 2m + 3n = 6 Add '-2m' to each side of the equation. 9i + 2m + -2m + 3n = 6 + -2m Combine like terms: 2m + -2m = 0 9i + 0 + 3n = 6 + -2m 9i + 3n = 6 + -2m Add '-3n' to each side of the equation. 9i + 3n + -3n = 6 + -2m + -3n Combine like terms: 3n + -3n = 0 9i + 0 = 6 + -2m + -3n 9i = 6 + -2m + -3n Divide each side by '9'. i = 0.6666666667 + -0.2222222222m + -0.3333333333n Simplifying i = 0.6666666667 + -0.2222222222m + -0.3333333333n
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