Algebra with complex numbers (i) My professor has assigned this problem:
Let r be a real number.  By using r = r + 0i, confirm that r(a + bi) = (ra) + (rb)i.
My understanding is that this looks at distributive property, but I do not understand how r = r + 0i relates.  Could someone provide a jumping off point?  I don't want/ need the entire problem solved... Just somewhere to start.
Thanks in advance.

I guess the professor defined "complex-multiplication" operation using "real-multiplication" as follows:

$(a+ib) \cdot (c+ id):= (ac-bd) + i(ad+bc)$.

Hence, $r\cdot (a+ib) = (r+i0)\cdot (a+ib)= (ra -0b) + i(rb + 0a)= (ra)+ i(rb)$.
