**Conversions to and from polar coordinates**

:func:`phase(z) <phase>` Return the phase of *z*

:func:`polar(z) <polar>` Return the representation of *z* in polar coordinates

:func:`rect(r, phi) <rect>` Return the complex number *z* with polar coordinates *r* and *phi*

**Power and logarithmic functions**

:func:`exp(z) <exp>` Return *e* raised to the power *z*

:func:`log(z[, base]) <log>` Return the logarithm of *z* to the given *base* (*e* by default)

:func:`log10(z) <log10>` Return the base-10 logarithm of *z*

:func:`sqrt(z) <sqrt>` Return the square root of *z*

**Trigonometric functions**

:func:`acos(z) <acos>` Return the arc cosine of *z*

:func:`asin(z) <asin>` Return the arc sine of *z*

:func:`atan(z) <atan>` Return the arc tangent of *z*

:func:`cos(z) <cos>` Return the cosine of *z*

:func:`sin(z) <sin>` Return the sine of *z*

:func:`tan(z) <tan>` Return the tangent of *z*

**Hyperbolic functions**

:func:`acosh(z) <acosh>` Return the inverse hyperbolic cosine of *z*

:func:`asinh(z) <asinh>` Return the inverse hyperbolic sine of *z*

:func:`atanh(z) <atanh>` Return the inverse hyperbolic tangent of *z*

:func:`cosh(z) <cosh>` Return the hyperbolic cosine of *z*

:func:`sinh(z) <sinh>` Return the hyperbolic sine of *z*

:func:`tanh(z) <tanh>` Return the hyperbolic tangent of *z*

**Classification functions**

:func:`isfinite(z) <isfinite>` Check if all components of *z* are finite

:func:`isinf(z) <isinf>` Check if any component of *z* is infinite

:func:`isnan(z) <isnan>` Check if any component of *z* is a NaN

:func:`isclose(a, b, *, rel_tol, abs_tol) <isclose>` Check if the values *a* and *b* are close to each other

**Constants**

:data:`pi` *π* = 3.141592...

:data:`e` *e* = 2.718281...

:data:`tau` *τ* = 2\ *π* = 6.283185...

:data:`inf` Positive infinity

:data:`infj` Pure imaginary infinity

:data:`nan` "Not a number" (NaN)

:data:`nanj` Pure imaginary NaN