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Simplifying (-6 + -7i) + -1(1 + 3i) = 0 Remove parenthesis around (-6 + -7i) -6 + -7i + -1(1 + 3i) = 0 -6 + -7i + (1 * -1 + 3i * -1) = 0 -6 + -7i + (-1 + -3i) = 0 Reorder the terms: -6 + -1 + -7i + -3i = 0 Combine like terms: -6 + -1 = -7 -7 + -7i + -3i = 0 Combine like terms: -7i + -3i = -10i -7 + -10i = 0 Solving -7 + -10i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -10i = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -10i = 0 + 7 -10i = 0 + 7 Combine like terms: 0 + 7 = 7 -10i = 7 Divide each side by '-10'. i = -0.7 Simplifying i = -0.7
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