# Length of a complex vector

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1. Feb 28, 2017

### David932

1. I am trying to calculate the length of a complex vector which has K and Rho components. Rho is a two dimensional position vector and K is the two dimensional vector in the Fourier space.

2. The relevant equation and the attempted solution are in the form of an image attached herewith. Please anyone can guide me in a step by step way to the correct solution.

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2. Mar 2, 2017

### stevendaryl

Staff Emeritus
If you have a complex vector $\vec{A}$, there are two different things you might mean by the "length". You might mean:

$|A| = \sqrt{A \cdot A}$
(which is the usual notion of the length of a real vector)

$|A| = \sqrt{A^* \cdot A}$

The first one is not guaranteed to be a positive number, or even a real number. So the second is a better indication of the magnitude of vector $A$. However, it's not clear that it should be considered the "length". What is your purpose in calculating the length, so that we can help say what expression for length is appropriate?

3. Mar 2, 2017

### haruspex

It seems natural to me that the magnitude $||\vec x||$ of a vector (xi) over any field would be defined as $||\vec x||^2=\Sigma ||x_i||^2$ where ||xi|| is the magnitude of the field element. Any other way would be strange.

4. Mar 2, 2017

### stevendaryl

Staff Emeritus
Sure, but people don't usually use the word "length" to mean "magnitude" except for real vectors.