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Simplifying (-10 + i)(-10 + -1i) = 0 Multiply (-10 + i) * (-10 + -1i) (-10(-10 + -1i) + i(-10 + -1i)) = 0 ((-10 * -10 + -1i * -10) + i(-10 + -1i)) = 0 ((100 + 10i) + i(-10 + -1i)) = 0 (100 + 10i + (-10 * i + -1i * i)) = 0 (100 + 10i + (-10i + -1i2)) = 0 Combine like terms: 10i + -10i = 0 (100 + 0 + -1i2) = 0 (100 + -1i2) = 0 Solving 100 + -1i2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + -1i2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -1i2 = 0 + -100 -1i2 = 0 + -100 Combine like terms: 0 + -100 = -100 -1i2 = -100 Divide each side by '-1'. i2 = 100 Simplifying i2 = 100 Take the square root of each side: i = {-10, 10}
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