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Determine the real numbers x and y for which the complex numbers z1 = 9y² - 4 - 10 i x and z2 = 8y² - 20 i are complex conjugates of each other.

1. x = 2, y = 2
2. x = -2, y = 2
3. x = 2, y = -2
4. x = 2, y = 2 or x = 2, y = -2

Correct answer: x = 2, y = 2 or x = 2, y = -2

Solution

Conjugate condition requires equal real parts (9y² - 4 = 8y²) and imaginary parts that are negatives of each other (-10x = +20 from conj(z2)=8y²+20i), giving x = 2 and y = +-2.

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