Question Detail

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=0, impossible. So the equality is false. The only way both are equal is if the number is real, which would require the imaginary part to be 0. Possibly the intended was to find the product or something else. Option C is 0 + (28/25)i, a pure imaginary, which is a common result from a different operation.