# 9.3. `cmath` ——关于复数的数学函数¶

This module is always available. It provides access to mathematical functions for complex numbers. The functions in this module accept integers, floating-point numbers or complex numbers as arguments. They will also accept any Python object that has either a `__complex__()` or a `__float__()` method: these methods are used to convert the object to a complex or floating-point number, respectively, and the function is then applied to the result of the conversion.

## 9.3.1. 到极坐标和从极坐标的转换¶

```z == z.real + z.imag*1j
```

`cmath.``phase`(x)

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 lies in the range [-π, π], and the branch cut for this operation lies along the negative real axis, continuous from above. On systems with support for signed zeros (which includes most systems in current use), this means that the sign of the result is the same as the sign of `x.imag`, even when `x.imag` is zero:

```>>> phase(complex(-1.0, 0.0))
3.141592653589793
>>> phase(complex(-1.0, -0.0))
-3.141592653589793
```

`cmath.``polar`(x)

`cmath.``rect`(r, phi)

## 9.3.2. 幂函数与对数函数¶

`cmath.``exp`(x)

Return the exponential value `e**x`.

`cmath.``log`(x[, base])

`cmath.``log10`(x)

`cmath.``sqrt`(x)

## 9.3.3. 三角函数¶

`cmath.``acos`(x)

`cmath.``asin`(x)

`cmath.``atan`(x)

`cmath.``cos`(x)

`cmath.``sin`(x)

`cmath.``tan`(x)

## 9.3.4. 双曲函数¶

`cmath.``acosh`(x)

`cmath.``asinh`(x)

`cmath.``atanh`(x)

`cmath.``cosh`(x)

`cmath.``sinh`(x)

`cmath.``tanh`(x)

## 9.3.5. 分类函数¶

`cmath.``isfinite`(x)

3.2 新版功能.

`cmath.``isinf`(x)

`cmath.``isnan`(x)

`cmath.``isclose`(a, b, *, rel_tol=1e-09, abs_tol=0.0)

ab 的值比较接近则返回 `True`，否则返回 `False`

rel_tol 是相对容差 —— 它是 ab 之间允许的最大差值，相对于 ab 的较大绝对值。例如，要设置5％的容差，请传递 `rel_tol=0.05` 。默认容差为 `1e-09`，确保两个值在大约9位十进制数字内相同。 rel_tol 必须大于零。

abs_tol 是最小绝对容差 —— 对于接近零的比较很有用。 abs_tol 必须至少为零。

IEEE 754特殊值 `NaN``inf``-inf` 将根据IEEE规则处理。具体来说， `NaN` 不被认为接近任何其他值，包括 `NaN``inf``-inf` 只被认为接近自己。

3.5 新版功能.

PEP 485 —— 用于测试近似相等的函数

## 9.3.6. 常量¶

`cmath.``pi`

`cmath.``e`

`cmath.``tau`

3.6 新版功能.

`cmath.``inf`

3.6 新版功能.

`cmath.``infj`

3.6 新版功能.

`cmath.``nan`

3.6 新版功能.

`cmath.``nanj`

3.6 新版功能.

Kahan, W: Branch cuts for complex elementary functions; or, Much ado about nothing’s sign bit. In Iserles, A., and Powell, M. (eds.), The state of the art in numerical analysis. Clarendon Press (1987) pp165–211.