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Simplifying (6 + -5i) + -1(7 + 3i) = 0 Remove parenthesis around (6 + -5i) 6 + -5i + -1(7 + 3i) = 0 6 + -5i + (7 * -1 + 3i * -1) = 0 6 + -5i + (-7 + -3i) = 0 Reorder the terms: 6 + -7 + -5i + -3i = 0 Combine like terms: 6 + -7 = -1 -1 + -5i + -3i = 0 Combine like terms: -5i + -3i = -8i -1 + -8i = 0 Solving -1 + -8i = 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 + 1 + -8i = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -8i = 0 + 1 -8i = 0 + 1 Combine like terms: 0 + 1 = 1 -8i = 1 Divide each side by '-8'. i = -0.125 Simplifying i = -0.125
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