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Simplifying 6(4i + 3) = 6(5i + -2) Reorder the terms: 6(3 + 4i) = 6(5i + -2) (3 * 6 + 4i * 6) = 6(5i + -2) (18 + 24i) = 6(5i + -2) Reorder the terms: 18 + 24i = 6(-2 + 5i) 18 + 24i = (-2 * 6 + 5i * 6) 18 + 24i = (-12 + 30i) Solving 18 + 24i = -12 + 30i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-30i' to each side of the equation. 18 + 24i + -30i = -12 + 30i + -30i Combine like terms: 24i + -30i = -6i 18 + -6i = -12 + 30i + -30i Combine like terms: 30i + -30i = 0 18 + -6i = -12 + 0 18 + -6i = -12 Add '-18' to each side of the equation. 18 + -18 + -6i = -12 + -18 Combine like terms: 18 + -18 = 0 0 + -6i = -12 + -18 -6i = -12 + -18 Combine like terms: -12 + -18 = -30 -6i = -30 Divide each side by '-6'. i = 5 Simplifying i = 5
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