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Simplifying (-5 + -8i) + -8 + -1(-7 + -2i) = 0 Remove parenthesis around (-5 + -8i) -5 + -8i + -8 + -1(-7 + -2i) = 0 -5 + -8i + -8 + (-7 * -1 + -2i * -1) = 0 -5 + -8i + -8 + (7 + 2i) = 0 Reorder the terms: -5 + -8 + 7 + -8i + 2i = 0 Combine like terms: -5 + -8 = -13 -13 + 7 + -8i + 2i = 0 Combine like terms: -13 + 7 = -6 -6 + -8i + 2i = 0 Combine like terms: -8i + 2i = -6i -6 + -6i = 0 Solving -6 + -6i = 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 + -6i = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -6i = 0 + 6 -6i = 0 + 6 Combine like terms: 0 + 6 = 6 -6i = 6 Divide each side by '-6'. i = -1 Simplifying i = -1
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