Dot Product Calculator Quandry

[infraray]

I'm going nuts here and I can't figure this out. I have two complex vectors:
A=(1+i)x + (1)y +(i)z
B=(4-i)x +(0)y + (2-2i)z
If I do the dot product of these on my calculator I get 1 + 7i, however when I do this by hand I keep getting 7 +5i. What am I doing wrong? When figuring this out by hand I am going by the assumption that AB=AxBx + AyBy + AzBz.

 

[Hurkyl]

Are you using parentheses properly?

 

[infraray]

I figured it out. I need to take the conjugate of the second vector. This is sure going to get confusing with Quantum Mechanics!

 

[uart]

I figured it out. I need to take the conjugate of the second vector.

Yes that's correct, for a complex inner product you take the conjugate of the second argument. It's defined that way so that if you take the inner product of a vector with itself then you'll always end up with just a real number. This real number is called the "norm" and is a generalized measure of the length of the vector.