The following functions can be used to convert from the native
rectangular coordinates to polar coordinates and back.
-.. function:: phase(x)
+.. function:: phase(z)
- Return the phase of *x* (also known as the *argument* of *x*), as a float.
- ``phase(x)`` is equivalent to ``math.atan2(x.imag, x.real)``. The result
+ Return the phase of *z* (also known as the *argument* of *z*), as a float.
+ ``phase(z)`` is equivalent to ``math.atan2(z.imag, z.real)``. The result
lies in the range [-\ *π*, *π*], and the branch cut for this operation lies
along the negative real axis. The sign of the result is the same as the
- sign of ``x.imag``, even when ``x.imag`` is zero::
+ sign of ``z.imag``, even when ``z.imag`` is zero::
>>> phase(complex(-1.0, 0.0))
3.141592653589793
.. note::
- The modulus (absolute value) of a complex number *x* can be
+ The modulus (absolute value) of a complex number *z* can be
computed using the built-in :func:`abs` function. There is no
separate :mod:`cmath` module function for this operation.
-.. function:: polar(x)
+.. function:: polar(z)
- Return the representation of *x* in polar coordinates. Returns a
- pair ``(r, phi)`` where *r* is the modulus of *x* and phi is the
- phase of *x*. ``polar(x)`` is equivalent to ``(abs(x),
- phase(x))``.
+ Return the representation of *z* in polar coordinates. Returns a
+ pair ``(r, phi)`` where *r* is the modulus of *z* and *phi* is the
+ phase of *z*. ``polar(z)`` is equivalent to ``(abs(z),
+ phase(z))``.
.. function:: rect(r, phi)
- Return the complex number *x* with polar coordinates *r* and *phi*.
+ Return the complex number *z* with polar coordinates *r* and *phi*.
Equivalent to ``complex(r * math.cos(phi), r * math.sin(phi))``.
Power and logarithmic functions
-------------------------------
-.. function:: exp(x)
+.. function:: exp(z)
- Return *e* raised to the power *x*, where *e* is the base of natural
+ Return *e* raised to the power *z*, where *e* is the base of natural
logarithms.
-.. function:: log(x[, base])
+.. function:: log(z[, base])
- Returns the logarithm of *x* to the given *base*. If the *base* is not
- specified, returns the natural logarithm of *x*. There is one branch cut,
+ Return the logarithm of *z* to the given *base*. If the *base* is not
+ specified, returns the natural logarithm of *z*. There is one branch cut,
from 0 along the negative real axis to -∞.
-.. function:: log10(x)
+.. function:: log10(z)
- Return the base-10 logarithm of *x*. This has the same branch cut as
+ Return the base-10 logarithm of *z*. This has the same branch cut as
:func:`log`.
-.. function:: sqrt(x)
+.. function:: sqrt(z)
- Return the square root of *x*. This has the same branch cut as :func:`log`.
+ Return the square root of *z*. This has the same branch cut as :func:`log`.
Trigonometric functions
-----------------------
-.. function:: acos(x)
+.. function:: acos(z)
- Return the arc cosine of *x*. There are two branch cuts: One extends right
+ Return the arc cosine of *z*. There are two branch cuts: One extends right
from 1 along the real axis to ∞. The other extends left from -1 along the
real axis to -∞.
-.. function:: asin(x)
+.. function:: asin(z)
- Return the arc sine of *x*. This has the same branch cuts as :func:`acos`.
+ Return the arc sine of *z*. This has the same branch cuts as :func:`acos`.
-.. function:: atan(x)
+.. function:: atan(z)
- Return the arc tangent of *x*. There are two branch cuts: One extends from
+ Return the arc tangent of *z*. There are two branch cuts: One extends from
``1j`` along the imaginary axis to ``∞j``. The other extends from ``-1j``
along the imaginary axis to ``-∞j``.
-.. function:: cos(x)
+.. function:: cos(z)
- Return the cosine of *x*.
+ Return the cosine of *z*.
-.. function:: sin(x)
+.. function:: sin(z)
- Return the sine of *x*.
+ Return the sine of *z*.
-.. function:: tan(x)
+.. function:: tan(z)
- Return the tangent of *x*.
+ Return the tangent of *z*.
Hyperbolic functions
--------------------
-.. function:: acosh(x)
+.. function:: acosh(z)
- Return the inverse hyperbolic cosine of *x*. There is one branch cut,
+ Return the inverse hyperbolic cosine of *z*. There is one branch cut,
extending left from 1 along the real axis to -∞.
-.. function:: asinh(x)
+.. function:: asinh(z)
- Return the inverse hyperbolic sine of *x*. There are two branch cuts:
+ Return the inverse hyperbolic sine of *z*. There are two branch cuts:
One extends from ``1j`` along the imaginary axis to ``∞j``. The other
extends from ``-1j`` along the imaginary axis to ``-∞j``.
-.. function:: atanh(x)
+.. function:: atanh(z)
- Return the inverse hyperbolic tangent of *x*. There are two branch cuts: One
+ Return the inverse hyperbolic tangent of *z*. There are two branch cuts: One
extends from ``1`` along the real axis to ``∞``. The other extends from
``-1`` along the real axis to ``-∞``.
-.. function:: cosh(x)
+.. function:: cosh(z)
- Return the hyperbolic cosine of *x*.
+ Return the hyperbolic cosine of *z*.
-.. function:: sinh(x)
+.. function:: sinh(z)
- Return the hyperbolic sine of *x*.
+ Return the hyperbolic sine of *z*.
-.. function:: tanh(x)
+.. function:: tanh(z)
- Return the hyperbolic tangent of *x*.
+ Return the hyperbolic tangent of *z*.
Classification functions
------------------------
-.. function:: isfinite(x)
+.. function:: isfinite(z)
- Return ``True`` if both the real and imaginary parts of *x* are finite, and
+ Return ``True`` if both the real and imaginary parts of *z* are finite, and
``False`` otherwise.
.. versionadded:: 3.2
-.. function:: isinf(x)
+.. function:: isinf(z)
- Return ``True`` if either the real or the imaginary part of *x* is an
+ Return ``True`` if either the real or the imaginary part of *z* is an
infinity, and ``False`` otherwise.
-.. function:: isnan(x)
+.. function:: isnan(z)
- Return ``True`` if either the real or the imaginary part of *x* is a NaN,
+ Return ``True`` if either the real or the imaginary part of *z* is a NaN,
and ``False`` otherwise.