
Derek F. answered 01/13/16
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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.
Michael J.
01/13/16