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Simplifying (7i + -3j) + -1(-2i + 9j) = 0 Remove parenthesis around (7i + -3j) 7i + -3j + -1(-2i + 9j) = 0 7i + -3j + (-2i * -1 + 9j * -1) = 0 7i + -3j + (2i + -9j) = 0 Reorder the terms: 7i + 2i + -3j + -9j = 0 Combine like terms: 7i + 2i = 9i 9i + -3j + -9j = 0 Combine like terms: -3j + -9j = -12j 9i + -12j = 0 Solving 9i + -12j = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '12j' to each side of the equation. 9i + -12j + 12j = 0 + 12j Combine like terms: -12j + 12j = 0 9i + 0 = 0 + 12j 9i = 0 + 12j Remove the zero: 9i = 12j Divide each side by '9'. i = 1.333333333j Simplifying i = 1.333333333j
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