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Simplifying (4 + 5i)(4 + -5i) = 0 Multiply (4 + 5i) * (4 + -5i) (4(4 + -5i) + 5i * (4 + -5i)) = 0 ((4 * 4 + -5i * 4) + 5i * (4 + -5i)) = 0 ((16 + -20i) + 5i * (4 + -5i)) = 0 (16 + -20i + (4 * 5i + -5i * 5i)) = 0 (16 + -20i + (20i + -25i2)) = 0 Combine like terms: -20i + 20i = 0 (16 + 0 + -25i2) = 0 (16 + -25i2) = 0 Solving 16 + -25i2 = 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 + -25i2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -25i2 = 0 + -16 -25i2 = 0 + -16 Combine like terms: 0 + -16 = -16 -25i2 = -16 Divide each side by '-25'. i2 = 0.64 Simplifying i2 = 0.64 Take the square root of each side: i = {-0.8, 0.8}
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