Understanding Complex Numbers in Dot Product Calculations

robertjford80 · Jun 24, 2012

Homework Statement

Worked solution showing the length of the vector with entries 1+i and 3: square root of the inner product with itself, then sqrt((1-i)(1+i) + (3)(3)) = sqrt(1 - i^2 + 9) = sqrt(11).

The Attempt at a Solution

do you see where it sees sqrt((1-i)(1+i)+9)?

It should be (1+i)(1+i)

Why isn't it?

tiny-tim · Jun 24, 2012

hi robertjford80!

robertjford80 said:

do you see where it sees sqrt((1-i)(1+i)+9)?

It should be (1+i)(1+i)

Why isn't it?

the complex inner product is defined with a conjugate on one side …

<a|b> = a*.b

(for real vectors, it makes no difference, so this isn't a different definition, it's the same as for real vectors

)

robertjford80 · Jun 24, 2012

ok thanks.

Understanding Complex Numbers in Dot Product Calculations

Homework Statement

The Attempt at a Solution

Discussion

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