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

[allegansveritatem]

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]

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!