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Simplifying (5 + 3i)(5 + -3i) = 0 Multiply (5 + 3i) * (5 + -3i) (5(5 + -3i) + 3i * (5 + -3i)) = 0 ((5 * 5 + -3i * 5) + 3i * (5 + -3i)) = 0 ((25 + -15i) + 3i * (5 + -3i)) = 0 (25 + -15i + (5 * 3i + -3i * 3i)) = 0 (25 + -15i + (15i + -9i2)) = 0 Combine like terms: -15i + 15i = 0 (25 + 0 + -9i2) = 0 (25 + -9i2) = 0 Solving 25 + -9i2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + -9i2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -9i2 = 0 + -25 -9i2 = 0 + -25 Combine like terms: 0 + -25 = -25 -9i2 = -25 Divide each side by '-9'. i2 = 2.777777778 Simplifying i2 = 2.777777778 Take the square root of each side: i = {-1.666666667, 1.666666667}
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