NEED SOME HELP!!


Suppose z = a + bi is a complex number, and w = x + yi is another complex number such that z +w is a real number and zw is also a real number. Show that w must be the conjugate of z. (Hint: A complex number is real if and only if its imaginarypart is 0; use this factto solve for x and y in terms of a and b.)


Thanks guys

start by expanding z+w and z*w in terms of a,b,x,y.

for z+w you'll have to collect like terms
for z*w you'll have to perform the multiplication

the problem tells you that for both cases you'll end up with no I left

hopefully you know what "conjugate" means (http://en.wikipedia.org/wiki/Complex_conjugate) so you should already know the relationship between a,b,x,y based on that. That means you'll know what your answer should look like.

Start from there and ask questions as you have them.