Coordination

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

A point in XY co ordinate can be presented as (X,Y) and (Z,θ) in Z θ co ordinate

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