# The absolute value ---- ## The magnitude --- # Le cercle unité le cercle trigonométrique ---- ## The unit circle --- # Un nombre complexe ---- ## A complex number --- # La partie réelle de $z$ ---- ## The real part of $z$ --- # La partie imaginaire de $z$ ---- ## The imaginary [ɪˈmædʒɪnəri] part of $z$ --- # $\mathbb{R}\subset \mathbb{C}$ ---- ## The set of real numbers is a subset of the set of complex numbers --- # Invented by Jean-Robert Argand (1768-1822) is used to represent numbers on the complex plane ---- ## The Argand diagram --- # The distance from the origin to the complex number on the Argand diagram ---- ## The modulus /ˈmɒdjələs/ of a complex number $z$ --- # The reflection of a complex number in the real axis ---- ## The conjugate /ˈkɒndʒəɡeɪt/ of a complex number --- # A polar /ˈpəʊlə(r)/ form of a complex number $z=x+y\text{i}$ ---- ## $z=r\left[\cos(\theta)+\text{i}\sin(\theta)\right]$ where $r=|z|=\sqrt{x^2+y^2}$ and $\theta$ is an argument /ˈɑːɡjumənt/ of $z$ <style> .slides {background-image:url("https://raw.githubusercontent.com/tremulotmaths/latex/master/von_koch_transparent.png");} .slides h1 {padding:2em; font-family:Arial; background-color:#133E29; opacity: 0.9;color:white; font-size:1em!important;} .slides h2 {background:#131750 ; opacity: 0.9;padding : 2em 0.2em; color:white; font-size:1em!important;} .slides h4 {margin-bottom:1.5em} </style>