Computing Inner Products in C: Simplifying Complex Vector Calculations

[torquerotates]

Homework Statement

x=(2,1+i,i) and y=(2-i,2,1+2i)

Homework Equations

The Attempt at a Solution

um ok normally i would use <a,b>=|a||b|cos(theta). But these are complex numbers. I have no clue how to do this.

 

[Hurkyl]

Surely you have a definition to appeal to?

(and I'm pretty sure that <a,b>=|a||b|cos(theta) isn't it -- and even if that equation were correct, it is rare that you'd actually want to use it to compute an inner product)

 

[D H]

Suppose instead you were just working with real vectors -- say (2,20,2) and (10,1,1). There is no need to compute the angle between these vectors. There is a much easier way to do this. What is another way to compute the inner product that |a||b|cos(theta)? How would you generalize this to complex numbers?

And finally, what is in your class notes and text? I am quite certain your instructor does not expect you to derive the formula for computing the inner product in C³. He or she expects you to use something you have already been taught.