# U(dot)U != ||U||^2 help?

1. Mar 31, 2009

### SoulofLoneWlf

1. The problem statement, all variables and given/known data

well i am told basicly this
|u|^2 = U dot U except when in using imaginary numbers
i tried using the example below and a few others but it seems to always work for me :/
but i need the process or to show this is not true

2. Relevant equations

||u|| = U dot U in general not complex :/

3. The attempt at a solution

2i + 5

2. Apr 1, 2009

### CompuChip

What are u and U?
Are they the same (U = u)?
Is u a vector, of which |u| is the norm, or just a number of which |u| is the absolute value (for real numbers) or the modulus (for complex ones). Or is it a matrix, for which |u| is some matrix norm?

If it is a number, it's rather easy to show.
The modulus (length) of 2i + 5 is $\sqrt{2^2 + 5^2}$ which is not equal to (2i + 5)^2.

In general, the correct expression is
|u|^2 = u . u*
where u* is the complex conjugate of u.