Please help

[cbbrown18]

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.)



If any one can help me solve this problem i would really appreciate it!!!

Thanks Guys

[OfficeShredder]

From the information, what can you deduce about a,b,x and y by adding w and z together? (z+w = a+x + (b+y)i )

[HallsofIvy]

"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 fact to solve for x and y in terms of a and b.) "

Okay, WHAT are z+w and zw in terms of a, b, x, and y? In other words, DO the addition and multiplication. Then set the two imaginary parts equal to 0.