NUMBER:
$Unique\; sequence\; of\; elements\; which\; used\; to\; count\; the\; collection\; of\; individuals\; OR\;$
$Mathematical\; object\; used\; to\; count\;, \;measure\; and\; label .$
TYPES OF NUMBER
$NATURAL\; NUMBER:$ $\mathbb{N}=\{1,2,3,...\}$
$WHOLE\; NUMBER:$ $\mathbb{W}=\{0,1,2,3,...\}$
$INTEGER:$ $\mathbb{Z}=\{0,±1,±2,…\}$
$RATIONAL\; NUMBER:$ $\mathbb{Q}=\{x|x =p/q\; and\; p,q\in \mathbb{Z} ,q\neq 0\}$
$IRRATIONAL\; NUMBER:$ $ \mathbb{Q}^{'}=\{x|x\neq p/q\; and\; p,q\in\mathbb{Z},q\neq 0\}$
$REAL\; NUMBER:$ $\mathbb{R}=\mathbb{Q}\cup\mathbb{Q}^{'}$
$COMPLEX\; NUMBER$ $\mathbb{C}=\{x+\iota y|x,y\in R\}\; where\; \iota\; is\; imaginary\; unit.$
NOTE:
$\star\;\mathbb{N}\subset \mathbb{W}\subset \mathbb{Z}\subset \mathbb{Q}\subset \mathbb{R}\subset \mathbb{C}$
NUMBER THEORY (HIGH ARITHMETIC):
$Mathematical\; theory\; that\; studies\; the\; properties\; and\; relation\; of\; integers.$
POLAR FORM OF COMPLEX NUMBER
$Z=x+iy=r(\cos\theta+\iota\sin\theta)=rcis\theta$
$Where\; r=|Z|=\sqrt{(x^2+y^2 )}\;and$
$Principle\; Value\; \theta=\tan^{-1}(\frac{y}{x})=Arg(Z) \;\;0\leq\theta\leq2\pi$
$Normal \;Value\; arg(Z)=Arg(Z)+2n\pi \;\;-\pi\leq\theta\leq\pi$
$\circ\;This\; is\; polar\; form\; of\; (x,y)\; in\; polar \;co-ordinates\; (r,\theta)$