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Simplifying 3i + 4(3i + -5) = 28 + -1i Reorder the terms: 3i + 4(-5 + 3i) = 28 + -1i 3i + (-5 * 4 + 3i * 4) = 28 + -1i 3i + (-20 + 12i) = 28 + -1i Reorder the terms: -20 + 3i + 12i = 28 + -1i Combine like terms: 3i + 12i = 15i -20 + 15i = 28 + -1i Solving -20 + 15i = 28 + -1i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add 'i' to each side of the equation. -20 + 15i + i = 28 + -1i + i Combine like terms: 15i + i = 16i -20 + 16i = 28 + -1i + i Combine like terms: -1i + i = 0 -20 + 16i = 28 + 0 -20 + 16i = 28 Add '20' to each side of the equation. -20 + 20 + 16i = 28 + 20 Combine like terms: -20 + 20 = 0 0 + 16i = 28 + 20 16i = 28 + 20 Combine like terms: 28 + 20 = 48 16i = 48 Divide each side by '16'. i = 3 Simplifying i = 3
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