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Simplifying 7i + 24 = 4i + 5(-4 + 5i) Reorder the terms: 24 + 7i = 4i + 5(-4 + 5i) 24 + 7i = 4i + (-4 * 5 + 5i * 5) 24 + 7i = 4i + (-20 + 25i) Reorder the terms: 24 + 7i = -20 + 4i + 25i Combine like terms: 4i + 25i = 29i 24 + 7i = -20 + 29i Solving 24 + 7i = -20 + 29i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-29i' to each side of the equation. 24 + 7i + -29i = -20 + 29i + -29i Combine like terms: 7i + -29i = -22i 24 + -22i = -20 + 29i + -29i Combine like terms: 29i + -29i = 0 24 + -22i = -20 + 0 24 + -22i = -20 Add '-24' to each side of the equation. 24 + -24 + -22i = -20 + -24 Combine like terms: 24 + -24 = 0 0 + -22i = -20 + -24 -22i = -20 + -24 Combine like terms: -20 + -24 = -44 -22i = -44 Divide each side by '-22'. i = 2 Simplifying i = 2
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