Number Systems

Number Systems

Any number that can be expressed as a fraction is a rational

Any number that can not be expressed as a fraction is irrational

Any number that is the solution of an equation is algebraic

Any number that is not the solution of an equation is transcendental

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

angles anticlockwise are positive

angles 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

Loci in the Argand Diagram

Circle with centre (a,b) and radius r has equation

(x-a)^2+((y-b)^2=r^2

Cartesian Equation

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

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