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The Python cmath.sinh() function returns the complex hyperbolic sine of a complex number z. It is a function on complex plane, and has no branch cuts. It is periodic with respect to the imaginary component, with period 2𝜋i.

Mathematically, it can be expressed as:

complex sinh




z Required. Specify a number to find the complex hyperbolic sine of

Return Value

Returns the complex hyperbolic sine of z.


In the below example, sinh() function is used to find out the complex hyperbolic sine of the given number.

import cmath

z1 = 2 + 2j
z2 = 2
z3 = 2j

print("cmath.sinh(z1):", cmath.sinh(z1))
print("cmath.sinh(z2):", cmath.sinh(z2))
print("cmath.sinh(z3):", cmath.sinh(z3))

The output of the above code will be:

cmath.sinh(z1): (-1.5093064853236158+3.4209548611170133j)
cmath.sinh(z2): (3.626860407847019+0j)
cmath.sinh(z3): (-0+0.9092974268256817j)

❮ Python cMath Module