In [1]:

    

import cmath
import math


    

In [2]:

    

c = 1 + 1j


    

In [3]:

    

print(math.atan2(c.imag, c.real))


    

    




0.7853981633974483

In [4]:

    

print(cmath.phase(c))


    

    




0.7853981633974483

In [5]:

    

print(cmath.phase(c) == math.atan2(c.imag, c.real))


    

    




True

In [6]:

    

print(math.degrees(cmath.phase(c)))


    

    




45.0

In [7]:

    

c = 1 + 1j

print(cmath.polar(c))
print(type(cmath.polar(c)))


    

    




(1.4142135623730951, 0.7853981633974483)
<class 'tuple'>

In [8]:

    

print(cmath.polar(c)[0] == abs(c))


    

    




True

In [9]:

    

print(cmath.polar(c)[1] == cmath.phase(c))


    

    




True

In [10]:

    

print(cmath.rect(1, 1))


    

    




(0.5403023058681398+0.8414709848078965j)

In [11]:

    

print(cmath.rect(1, 0))


    

    




(1+0j)

In [12]:

    

print(cmath.rect(cmath.polar(c)[0], cmath.polar(c)[1]))


    

    




(1.0000000000000002+1j)

In [13]:

    

r = 2
ph = math.pi


    

In [14]:

    

print(cmath.rect(r, ph).real == r * math.cos(ph))


    

    




True

In [15]:

    

print(cmath.rect(r, ph).imag == r * math.sin(ph))


    

    




True

In [16]:

    

print((-3 + 4j) ** 0.5)


    

    




(1.0000000000000002+2j)

In [17]:

    

print((-1) ** 0.5)


    

    




(6.123233995736766e-17+1j)

In [18]:

    

print(cmath.sqrt(-3 + 4j))


    

    




(1+2j)

In [19]:

    

print(cmath.sqrt(-1))


    

    




1j