# Complex math

Complex Math can be performed in Python easily for complex math functions. Learn more about complex match commands and codes here.

## Complex Math: Advanced complex arithmetic

The module cmath includes additional functions to use complex numbers.

import cmath

This module can calculate the phase of a complex number, in radians:

`z = 2+3j # A complex numbercmath.phase(z) # 0.982793723247329`

It allows the conversion between the cartesian (rectangular) and polar representations of complex numbers:

`cmath.polar(z) # (3.605551275463989, 0.982793723247329)cmath.rect(2, cmath.pi/2) # (0+2j)`

The module contains the complex version of

Exponential and logarithmic functions (as usual, log is the natural logarithm and log10 the decimal logarithm):

`cmath.exp(z) # (-7.315110094901103+1.0427436562359045j)cmath.log(z) # (1.2824746787307684+0.982793723247329j)cmath.log10(-100) # (2+1.3643763538418412j)`

Square roots:

`cmath.sqrt(z) # (1.6741492280355401+0.8959774761298381j)`

Trigonometric functions and their inverses:

`cmath.sin(z) # (9.15449914691143-4.168906959966565j)cmath.cos(z) # (-4.189625690968807-9.109227893755337j)cmath.tan(z) # (-0.003764025641504249+1.00323862735361j)cmath.asin(z) # (0.5706527843210994+1.9833870299165355j)cmath.acos(z) # (1.0001435424737972-1.9833870299165355j)cmath.atan(z) # (1.4099210495965755+0.22907268296853878j)cmath.sin(z)2 + cmath.cos(z)2 # (1+0j)`

Hyperbolic functions and their inverses:

`cmath.sinh(z) # (-3.59056458998578+0.5309210862485197j) cmath.cosh(z) # (-3.7245455049153224+0.5118225699873846j) cmath.tanh(z) # (0.965385879022133-0.009884375038322495j) cmath.asinh(z) # (0.5706527843210994+1.9833870299165355j) cmath.acosh(z) # (1.9833870299165355+1.0001435424737972j) cmath.atanh(z) # (0.14694666622552977+1.3389725222944935j) cmath.cosh(z)2 - cmath.sin(z)2 # (1+0j) cmath.cosh((0+1j)*z) - cmath.cos(z) # 0j`

## Complex Math: Basic complex arithmetic

Python has built-in support for complex arithmetic. The imaginary unit is denoted by j:

`z = 2+3j # A complex numberw = 1-7j # Another complex number`
`Complex numbers can be summed, subtracted, multiplied, divided and exponentiated:z + w # (3-4j)z - w # (1+10j)z * w # (23-11j)z / w # (-0.38+0.34j)z**3 # (-46+9j)`

Python can also extract the real and imaginary parts of complex numbers, and calculate their absolute value and conjugate:

`z.real # 2.0z.imag # 3.0abs(z) # 3.605551275463989z.conjugate() # (2-3j)`
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