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Simplifying (4 + 3i) * x(4 + -3i) = 0 Reorder the terms for easier multiplication: x(4 + 3i)(4 + -3i) = 0 Multiply (4 + 3i) * (4 + -3i) x(4(4 + -3i) + 3i * (4 + -3i)) = 0 x((4 * 4 + -3i * 4) + 3i * (4 + -3i)) = 0 x((16 + -12i) + 3i * (4 + -3i)) = 0 x(16 + -12i + (4 * 3i + -3i * 3i)) = 0 x(16 + -12i + (12i + -9i2)) = 0 Combine like terms: -12i + 12i = 0 x(16 + 0 + -9i2) = 0 x(16 + -9i2) = 0 (16 * x + -9i2 * x) = 0 Reorder the terms: (-9i2x + 16x) = 0 (-9i2x + 16x) = 0 Solving -9i2x + 16x = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-16x' to each side of the equation. -9i2x + 16x + -16x = 0 + -16x Combine like terms: 16x + -16x = 0 -9i2x + 0 = 0 + -16x -9i2x = 0 + -16x Remove the zero: -9i2x = -16x Divide each side by '-9x'. i2 = 1.777777778 Simplifying i2 = 1.777777778 Take the square root of each side: i = {-1.333333333, 1.333333333}
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