# what does this notation mean? "Verify (bar over)(z + w) = (bar over)(z) + (bar over)(w)" What are the bars?

#### allegansveritatem

##### Full Member
Well, that's mostly correct (accounting for a few typos). It is true that $$\displaystyle (a + bi)(a + bi) = (a + bi)^2 = a^2 + 2abi - b^2$$ ... but that's not what we have here. Did you notice the line over the second $$\displaystyle (a + bi)$$? Do you recall that the overline means "complex conjugate?" What is the complex conjugate of $$\displaystyle a + bi$$? Can you see why that means that the statement $$\displaystyle (a + bi)\overline{(a +bi)} = (a + bi)(a - bi)$$ is just a tautology?
No. I did not notice the overhead line. Again. You are right. The second term is the conjugate. Thanks for pointing that out. Yes, I can see the tautology. I have been just dumb2 working with this problem. But slowly I am getting it. Part of the trouble is I have not had much exposure to the concept of absolute value. I am working to remedy this ignorance.

#### ksdhart2

##### Senior Member
No worries. These things happen. There was one time I wrote as part of my workings that 2 times 3 is 5. It took me far too long to find my error. Talk about embarrassing!