Question Detail

The two fractions are conjugates. For them to be equal, the number must be real, implying the imaginary part is 0. Compute one: (5-2i)/(3-4i) = (5-2i)(3+4i)/(9+16) = (15+20i-6i-8i²)/25 = (15+14i+8)/25 = (23+14i)/25. Its conjugate is (23-14i)/25. They are equal only if 14i/25 = -14i/25, which implies 14=0, impossible. So the given equality is false unless the number is real. The only way both fractions are equal is if the number is real, which would require 14i=0, not possible. The question might have a misprint. Option C is 0 + (28/25)i, a pure imaginary. That is a common result from a different operation.