What is the Method for Finding the Magnitude of a Complex Vector?

[David932]

Homework Statement

Let a is a complex vector given by

a = 2π K - i ρ / α^2 ,

where ρ is a two dimensional position vector and K is the corresponding two dimensional vector in the Fourier space.

In order to find magnitude of this vector, i found that it is 4π^2 K^2 + ρ^2 / α^4 .
The logic I used to get my solution is
(magnitude of a)^2 = a.a*, where * denotes the complex conjugate.

Please can someone guide me to the correct step by step solution.Thanks

 

[BvU]

How can it be you have found the magnitude without going through the steps ?
What's the expression for the magnitude of a vector ?
What's the expression for the magnitude of a complex number ?
Are you aware of the PF rules and the guidelines that in fact disallow us to help you if you don't make an attempt at solution ?

 

[David932]

Hi BvU i edited my question and included the formula which I used for getting the answer.

 

[BvU]

And the formula did its work, so what is your question ?

 

[David932]

And the formula did its work, so what is your question ?

My question is whether the formula I used and the answer I got is correct or my logic has a conceptual mistake?

 

[BvU]

I think you are doing fine. For a vector you have the inner product and for a complex number you have the $|{\bf a}|^2= {\bf aa^*}$.
(so don't forget to take the square root at the end ... )

 

[David932]

I think you are doing fine. For a vector you have the inner product and for a complex number you have the $|{\bf a}|^2= {\bf aa^*}$.
(so don't forget to take the square root at the end ... )

Thanks for the reply. Yes, I should take the square root at the end.