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Simplifying (-3i + 4)(3i + 4) = 0 Reorder the terms: (4 + -3i)(3i + 4) = 0 Reorder the terms: (4 + -3i)(4 + 3i) = 0 Multiply (4 + -3i) * (4 + 3i) (4(4 + 3i) + -3i * (4 + 3i)) = 0 ((4 * 4 + 3i * 4) + -3i * (4 + 3i)) = 0 ((16 + 12i) + -3i * (4 + 3i)) = 0 (16 + 12i + (4 * -3i + 3i * -3i)) = 0 (16 + 12i + (-12i + -9i2)) = 0 Combine like terms: 12i + -12i = 0 (16 + 0 + -9i2) = 0 (16 + -9i2) = 0 Solving 16 + -9i2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + -9i2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -9i2 = 0 + -16 -9i2 = 0 + -16 Combine like terms: 0 + -16 = -16 -9i2 = -16 Divide each side by '-9'. i2 = 1.777777778 Simplifying i2 = 1.777777778 Take the square root of each side: i = {-1.333333333, 1.333333333}
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