# Vector quantities

## Introduction

The quantities available for post-processing can be scalar or vector quantities.

This section deals with vector quantities and recalls some definitions: complex notation, elliptical representation…

## Vector quantities (complex notation as rotating vectors)

Each component of a vector quantity can be written as a sinusoidal quantity:

; …

or, in complex notation:

; …

; …

where:

• is the modulus of the complex component
• is the argument (or the phase) of the complex component
• is the real part of the complex component
• is the imaginary part of the complex component

## Elliptical representation in 2D

In general case, the vector quantities are varying in function of time on ellipses.

For each point, the magnetic flux density can be written:

These are the parametric equations of an ellipse.

The two components of the magnetic flux density can be expressed depending on the ellipse characteristics, as follows:

• , where
• where

a is called “½ major axis” and b is called “½ minor axis