Arithmetic Course/Non Linear Function/Circular Function

Circular Function

Real Number

${\displaystyle {\frac {x^{2}}{a}}+{\frac {y^{2}}{b}}=1}$

When x = 0

${\displaystyle y=\pm {\sqrt {b}}}$

When y = 0

${\displaystyle x=\pm {\sqrt {a}}}$

Further, when

a = b . The function above is a Circular Function
a > b . The function above is a Elliptical Function
a < b . The function above is a Elliptical Function

Complex Number

${\displaystyle {\frac {x^{2}}{a}}-{\frac {y^{2}}{b}}=1}$

When x = 0

${\displaystyle y=\pm {\sqrt {-b}}}$
${\displaystyle y=\pm j{\sqrt {b}}}$

When y = 0

${\displaystyle x=\pm {\sqrt {-a}}}$
${\displaystyle y=\pm j{\sqrt {a}}}$

The function above is a Circular Function in a Complex number