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