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Simplifying -1i + (7 + -5i) + -3(2 + -3u) = 0 Remove parenthesis around (7 + -5i) -1i + 7 + -5i + -3(2 + -3u) = 0 -1i + 7 + -5i + (2 * -3 + -3u * -3) = 0 -1i + 7 + -5i + (-6 + 9u) = 0 Reorder the terms: 7 + -6 + -1i + -5i + 9u = 0 Combine like terms: 7 + -6 = 1 1 + -1i + -5i + 9u = 0 Combine like terms: -1i + -5i = -6i 1 + -6i + 9u = 0 Solving 1 + -6i + 9u = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -6i + -1 + 9u = 0 + -1 Reorder the terms: 1 + -1 + -6i + 9u = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6i + 9u = 0 + -1 -6i + 9u = 0 + -1 Combine like terms: 0 + -1 = -1 -6i + 9u = -1 Add '-9u' to each side of the equation. -6i + 9u + -9u = -1 + -9u Combine like terms: 9u + -9u = 0 -6i + 0 = -1 + -9u -6i = -1 + -9u Divide each side by '-6'. i = 0.1666666667 + 1.5u Simplifying i = 0.1666666667 + 1.5u
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