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Simplifying (3 + -8i) + -1(9 + -4i) = 4i + -12 Remove parenthesis around (3 + -8i) 3 + -8i + -1(9 + -4i) = 4i + -12 3 + -8i + (9 * -1 + -4i * -1) = 4i + -12 3 + -8i + (-9 + 4i) = 4i + -12 Reorder the terms: 3 + -9 + -8i + 4i = 4i + -12 Combine like terms: 3 + -9 = -6 -6 + -8i + 4i = 4i + -12 Combine like terms: -8i + 4i = -4i -6 + -4i = 4i + -12 Reorder the terms: -6 + -4i = -12 + 4i Solving -6 + -4i = -12 + 4i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-4i' to each side of the equation. -6 + -4i + -4i = -12 + 4i + -4i Combine like terms: -4i + -4i = -8i -6 + -8i = -12 + 4i + -4i Combine like terms: 4i + -4i = 0 -6 + -8i = -12 + 0 -6 + -8i = -12 Add '6' to each side of the equation. -6 + 6 + -8i = -12 + 6 Combine like terms: -6 + 6 = 0 0 + -8i = -12 + 6 -8i = -12 + 6 Combine like terms: -12 + 6 = -6 -8i = -6 Divide each side by '-8'. i = 0.75 Simplifying i = 0.75
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