Number Systems

Nodos de los diagramas

• Number Systems

• Any number that can be expressed as a fraction is a rationalAny number that can not be expressed as a fraction is irrationalAny number that is the solution of an equation is algebraicAny number that is not the solution of an equation is transcendental

• H Wmu Y (image/png)

• Complex numbers are represented using this.If y=0 ⇒ Z=x

• Argand Diagram

• The modulus of Z: The argument of Z:

• Measured in radians and anticlockwise

• Num Sys 6 (image/png)

• angles anticlockwise are positiveangles clockwise are negative

• Multiplication & Division

• Let Z˅1&Z˅2 be two complex numbers such that arg)Z˅1)=θ1 and arg(Z˅2)=θ2

• Num Sys 3a (image/png)

• Num Sys 3b (image/png)

• Num Sys 4a (image/png)

• Num Sys 4b (image/png)

• Loci in the Argand DiagramCircle with centre (a,b) and radius r has equation(x-a)^2+((y-b)^2=r^2

• Cartesian EquationThe Cartesian Equation of the locus of a point P is the equation that contains only x, y and constants

• Num Sys 5 (image/png)

• Num Sys 1 (image/png)

• Num Sys 2 (image/png)

• https://math.stackexchange.com/questions/153741/argand-diagram-quadrants-help