the conjugate of the sum of two complex numbers is equal to the sum of the conjugates of the two numbers.

here is the whole problem: the conjugate of the sum of two complex numbers is equal to the sum of the conjugates of the two numbers.  using a+bi and c+di to represent two complex numbers. verify this. 
 
i do not understand any of this. please help me and show me the equation and how to solve it. it is due by tomorrow morning.

the conjugate of a number is one that changes the sign of the imaginary portion. more formally, the complex conjugate of a complex number is a number with an equal real part and imaginary part equal in magnitude, but opposite in sign.
 
for example
 
the conjugate of 
 
3+4i
 
will be 
 
3-4i
 
in this case, you can verify with a few steps.
 
(a+bi) + (c+di) = a+c+i(b+d)
 
the conjugate of
 
 
a + c + i(b + d) is a + c - i(b + d)
 
now let's take the conjugate of the numbers and add them
 
a - bi + c - di = a + c - i(b + d)
 
as you can see, the conjugate of the sum is equal to the sum of the conjugates.
 
 
 
 

conjugates means that we have plus/minus sign.  recall the solution when using the quadratic formula.
 
 
first, we take the conjugate of the sum of two complex numbers. 
 
(a + bi) + (a + di) = 2a + (b + d)i
 
this is the sum of the complex numbers.  now take the conjugate of this sum.
 
the conjugate is          2a - (b + d)i

 
 
 
now we deal with the second part.  take the sum of the conjugates of the numbers.
 
(a - bi) + (a - di) =
 
2a - (b + d)i
 
 
the bolded results from both parts are the same.