Which pair of complex numbers has a real-number product?

(1 + 2i) (8i)

(1 + 2i) (2 - 5i)

(1 + 2i) (1 - 2i)

(1 + 2i) (4i)

I^2=-1

1. (1+2i) (8i) = 8i-16 (not a real number)

2. (1+2i) (2-5i) = 2-3i+10=12-3i (not a real number)

3. (1+2i) (1-2i) = 1+4=5 (real number)

4. (1+2i) (4i) = 4i-8 (not a real number)

So the answer is the third option choice.