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Simplifying (4 + -10i) + -1(7 + -9i) = 0 Remove parenthesis around (4 + -10i) 4 + -10i + -1(7 + -9i) = 0 4 + -10i + (7 * -1 + -9i * -1) = 0 4 + -10i + (-7 + 9i) = 0 Reorder the terms: 4 + -7 + -10i + 9i = 0 Combine like terms: 4 + -7 = -3 -3 + -10i + 9i = 0 Combine like terms: -10i + 9i = -1i -3 + -1i = 0 Solving -3 + -1i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1i = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1i = 0 + 3 -1i = 0 + 3 Combine like terms: 0 + 3 = 3 -1i = 3 Divide each side by '-1'. i = -3 Simplifying i = -3
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