Philip P. answered • 10/18/17

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For a complex number a + bi, the conjugate is a - bi. OK let's choose two complex numbers, 2 + 3i and 5 - 2i and unravel this mystery.

1) The "

**conjugate of the sum**" means to add the two complex numbers, then take the conjugate of the sum, as follows: 2 + 3i

+ (5 - 2i)

-------

7 + i

The sum is 7 + i. The "conjugate of the sum" is is

**7 - i**.2) The "

**sum of the conjugates**" means take the conjugates of the two numbers we started with, then add them. The conjugate of 2 + 3i is 2 - 3i. The conjugate of 5 - 2i is 5 + 2i. Now let's sum the conjugates:

2 - 3i

+ (5 + 2i)

------

**7 - i**

Which is the same answer we got in part 1 above. Hence the "conjugate of the sum" equals the "sum of the conjugates". Now you too can baffle your friends with your knowledge of complex numbers!