# Fundamental Mathematics/Arithmetic/Coordinate system

## Coordinate system

### Cartesian Coordinate

A point in Cartesian coordinate is expressed as

A (x,y)

### Polar Coordinate

A point in Cartesian coordinate is expressed as

A (r,${\displaystyle \theta }$)

### Conversion

${\displaystyle r={\sqrt {x^{2}+y^{2}}}}$
${\displaystyle \theta =Tan^{-1}{\frac {y}{x}}}$
${\displaystyle x=rCos\theta }$
${\displaystyle y=rSin\theta }$

## Real Number Coordination

A point in XY co ordinate can be presented as (${\displaystyle X,Y}$) and (${\displaystyle R,\theta }$) in R θ co ordinate

A , (${\displaystyle X,Y}$) , (${\displaystyle R,\theta }$)
 Scalar maths Vector Maths ${\displaystyle R\angle \theta ={\sqrt {X^{2}+Y^{2}}}\angle Tan^{-1}{\frac {Y}{X}}}$${\displaystyle R={\sqrt {X^{2}+Y^{2}}}}$${\displaystyle \theta =\angle Tan^{-1}{\frac {Y}{X}}}$ ${\displaystyle X(\theta )=RCos\theta }$${\displaystyle Y(\theta )=RSin\theta }$${\displaystyle R(\theta )=X(\theta )+Y(\theta )=R(Cos\theta +Sin\theta )}$${\displaystyle \nabla \cdot R(\theta )=X(\theta )=RCos\theta }$${\displaystyle \nabla \times R(\theta )=Y(\theta )=RSin\theta }$

## Complex Number Coordination

 ${\displaystyle Z.(X,jY),(Z,\theta )}$${\displaystyle Z^{*}.(X,-jY),(R,-\theta )}$ ${\displaystyle X(\theta )=ZCos\theta }$${\displaystyle jY(\theta )=jZSin\theta }$${\displaystyle -jY(\theta )=-jZSin\theta }$ ${\displaystyle Z\angle \theta ={\sqrt {X^{2}+Y^{2}}}\angle Tan^{-1}{\frac {Y}{X}}}$${\displaystyle Z\angle -\theta ={\sqrt {X^{2}+Y^{2}}}\angle -Tan^{-1}{\frac {Y}{X}}}$${\displaystyle Z={\sqrt {X^{2}+Y^{2}}}}$${\displaystyle \theta =\angle Tan^{-1}{\frac {Y}{X}}}$ ${\displaystyle Z(\theta )=X(\theta )+jY(\theta )=Z(Cos\theta +jSin\theta )}$${\displaystyle \nabla \cdot Z(\theta )=X(\theta )=ZCos\theta }$${\displaystyle \nabla \times Z(\theta )=jY(\theta )=jZSin\theta }$${\displaystyle Z^{*}(\theta )=X(\theta )-jY(\theta )=Z(Cos\theta -jSin\theta )}$${\displaystyle \nabla \cdot Z(\theta )=X(\theta )=Z^{*}Cos\theta }$${\displaystyle \nabla \times Z(\theta )=-jY(\theta )=jZ^{*}Sin\theta }$${\displaystyle Cos\theta ={\frac {Z(\theta )+Z^{*}(\theta )}{2}}}$${\displaystyle Sin\theta ={\frac {Z(\theta )-Z^{*}(\theta )}{2j}}}$${\displaystyle -Sin\theta ={\frac {Z^{*}(\theta )-Z^{(}\theta )}{2j}}}$