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Simplifying (2 + i)(2 + -1i) = 0 Multiply (2 + i) * (2 + -1i) (2(2 + -1i) + i(2 + -1i)) = 0 ((2 * 2 + -1i * 2) + i(2 + -1i)) = 0 ((4 + -2i) + i(2 + -1i)) = 0 (4 + -2i + (2 * i + -1i * i)) = 0 (4 + -2i + (2i + -1i2)) = 0 Combine like terms: -2i + 2i = 0 (4 + 0 + -1i2) = 0 (4 + -1i2) = 0 Solving 4 + -1i2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1i2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1i2 = 0 + -4 -1i2 = 0 + -4 Combine like terms: 0 + -4 = -4 -1i2 = -4 Divide each side by '-1'. i2 = 4 Simplifying i2 = 4 Take the square root of each side: i = {-2, 2}
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