» Complex Numbers
This site relies heavily on Javascript. You should enable it if you want the full experience. Learn more.

Complex Numbers

work in progress

Definition

Real numbers have a property specifying that for any real number r,

r ² > 0

Complex number is an extention of the real numbers, adding a number i satisfying the equation i ^ 2 = -1

A complex number is usually written in the form: a + bi

a and b are real numbers, a being call the real part, and b the imaginary part.

Two complex numbers a + bi and c + di are considered equal if :
a=c AND b=d

Operations

Addition

Adding two complex numbers is simply done by adding the real parts together and the imaginary parts together.

(a+bi) + (c+di) = (a+b) + (c+d)i

+ (Complex)

Subtraction

Subtracting two complex numbers is simply done by adding the real parts together and the imaginary parts together.

(a+bi) - (c+di) = (a-b) + (c-d)i

- (Complex)

Multiplication

To process multiplication, we use standard algebra rules:

(a + bi) * (c + di) = (a*c - b*d) + (a*d + b*c)i

decomposition:
(a + bi) * (c + di) = a*c + a*di + c * bi + bi * di = a*c + (a*d + b*c)i + b*d i² = (a*c - b*d) + (a*d + b*c)i

* (Complex)

Division

(a + bi) / (c + di) = ( (ac + bd + (bc - ad)i ) / (c² + d²)

/ (Complex)

anonymous user login

Shoutbox

~9h ago

beyon: tekcor: no, but I have a old Roland DXY-980 plotter depending on your needs

~2d ago

tekcor: Hey, does someone has an AxisDraw V3/A3 for sale?

~7d ago

nanotekt: vvvv+blender=lovvvve :D https://youtu.be/dUyeoi9mBIc

~7d ago

Patxi7: Pepper's Ghost & vvvv https://vimeo.com/632159133

~12d ago

mediadog: @manuelgonzalvez Needed to explicitly install VLC for VLC2; I use 3.0.6-win64 for stability.

~12d ago

mediadog: @manuelgonzalvez 42 getting crashes from DX11 VLC lib after last Win10 update. Switched to VLC2 plugin OK so far.

~14d ago

sunep: Looks interesting. Can't find a price though https://en.ids-imaging.com/ensenso-3d-camera-s-series.html

~24d ago

joreg: @guest re svg export: i'm afraid not.

~24d ago

joreg: @manuelgonzalvez what's stopping you? now is the time!

~24d ago

joreg: @schlonzo glad you like it!