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Simplifying 9(3i + -18) = 3(15i + 3) Reorder the terms: 9(-18 + 3i) = 3(15i + 3) (-18 * 9 + 3i * 9) = 3(15i + 3) (-162 + 27i) = 3(15i + 3) Reorder the terms: -162 + 27i = 3(3 + 15i) -162 + 27i = (3 * 3 + 15i * 3) -162 + 27i = (9 + 45i) Solving -162 + 27i = 9 + 45i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-45i' to each side of the equation. -162 + 27i + -45i = 9 + 45i + -45i Combine like terms: 27i + -45i = -18i -162 + -18i = 9 + 45i + -45i Combine like terms: 45i + -45i = 0 -162 + -18i = 9 + 0 -162 + -18i = 9 Add '162' to each side of the equation. -162 + 162 + -18i = 9 + 162 Combine like terms: -162 + 162 = 0 0 + -18i = 9 + 162 -18i = 9 + 162 Combine like terms: 9 + 162 = 171 -18i = 171 Divide each side by '-18'. i = -9.5 Simplifying i = -9.5
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