Applied mathematics/Coordination

Real Number Coordination

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

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

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

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