Find <x,y> in Inner Product Spaces: 8+5i

[snesnerd]

Let x = (2,1+i,i) and y = (2-i,2,1+2i). Find <x,y>

So my work is the following:

2(2-i) + (1+i)2 + i(1+2i) = 4+i, but my book says the correct answer is 8+5i. Hmmm what am I doing wrong?

 

[Dick]

Let x = (2,1+i,i) and y = (2-i,2,1+2i). Find <x,y>

So my work is the following:

2(2-i) + (1+i)2 + i(1+2i) = 4+i, but my book says the correct answer is 8+5i. Hmmm what am I doing wrong?

The inner product in complex spaces involves taking the complex conjugate of one of the vectors before you do the inner product. Look up your definition of inner product. Otherwise it's not a real inner product. <x,x> won't be greater than or equal to 0.