How do I prove that the conjugate of the product of two complex numbers is the product of their conjugates?

conjugate numbers = a1+b1i and a2+b2i


I really need help because i can't figure it out. And don't say I didn't try, because I spent a freakin' 30 minutes trying to figure out and I keep getting different signs! Thank you if you answer this!How do I prove that the conjugate of the product of two complex numbers is the product of their conjugates?
Multiply the numbers together. Since I can't do subscripts, I'll use a + bi and c + di





(a + bi)(c + di) = ac + bci + adi - bd = (ac - bd) + i(bc + ad)





The conjugate of their product is, then, (ac - bd) - i(bc + ad)





Now take their conjugates: a - bi, c - di, and multiply them





(a - bi)(c - di) = ac - bci - adi - bd = (ac - bd) - i(bc + ad)





Now compare your answers. QED