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Simplifying (3 + -4i)(3 + 4i) = 0 Multiply (3 + -4i) * (3 + 4i) (3(3 + 4i) + -4i * (3 + 4i)) = 0 ((3 * 3 + 4i * 3) + -4i * (3 + 4i)) = 0 ((9 + 12i) + -4i * (3 + 4i)) = 0 (9 + 12i + (3 * -4i + 4i * -4i)) = 0 (9 + 12i + (-12i + -16i2)) = 0 Combine like terms: 12i + -12i = 0 (9 + 0 + -16i2) = 0 (9 + -16i2) = 0 Solving 9 + -16i2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -16i2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -16i2 = 0 + -9 -16i2 = 0 + -9 Combine like terms: 0 + -9 = -9 -16i2 = -9 Divide each side by '-16'. i2 = 0.5625 Simplifying i2 = 0.5625 Take the square root of each side: i = {-0.75, 0.75}
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