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