Alternative representations of complex numbers


As mentioned in the latest post any complex number may be represented by an arrow in the complex plane. This number is unambiguously described by two numbers: its real part x and its imaginary part y. z= x+iy. This is called the Cartesian representation. (Rene Descartes)

From the figure below it is evident that

x = r cosφ

y = r sin φ  and thus z = r( cosφ + i sinφ) . This is called polar representation of the complex number z. r is the modulus of the vector z (i.e. its length) and φ is called the argument of z.    The modulus can be  computed by multiplying the  complex number z with its conjugated complex number z

By adding the  Taylor series for cos(x) and  i sin(x) we get the series expansion for the exponential function eix. This relation is called Euler’s formula.

This leads to the exponential representation of a complex number:

z= r e(iφ) 

This

 File:Complex conjugate picture.svg
Annonser

Om mattelararen

Licentiate of Philosophy in atomic Physics Master of Science in Physics
Det här inlägget postades i Imaginary numbers, matematik 4, matematik 5 och har märkts med etiketterna , , , . Bokmärk permalänken.

Kommentera

Fyll i dina uppgifter nedan eller klicka på en ikon för att logga in:

WordPress.com Logo

Du kommenterar med ditt WordPress.com-konto. Logga ut / Ändra )

Twitter-bild

Du kommenterar med ditt Twitter-konto. Logga ut / Ändra )

Facebook-foto

Du kommenterar med ditt Facebook-konto. Logga ut / Ändra )

Google+ photo

Du kommenterar med ditt Google+-konto. Logga ut / Ändra )

Ansluter till %s