In [1]:
import numpy as np
import sympy as sym
from IPython.display import display,Math
In [2]:
display(Math('x^2 + 1 = 0'))
display(Math('x^2 = -1'))
display(Math('x = \\pm \\sqrt 1'))
$\displaystyle x^2 + 1 = 0$
$\displaystyle x^2 = -1$
$\displaystyle x = \pm \sqrt 1$
In [3]:
print(1j)
print(np.sqrt(-1))
print(np.sqrt(-1,dtype='complex'))
print((-1)**(1/2))
print(sym.I)

1j
nan
1j
(6.123233995736766e-17+1j)
I

/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:2: RuntimeWarning: invalid value encountered in sqrt
In [4]:
real_part = 4
imag_part = -5

cn1 = np.complex(real_part,imag_part)
cn2 = real_part + 1j*imag_part

print(type(cn1))
print(cn1)
print(type(cn2))
print(cn2)

<class 'complex'>
(4-5j)
<class 'complex'>
(4-5j)
In [5]:
z1 = np.complex(4,5)
z2 = np.complex(3,2)

z1+z2
Out[5]:
(7+7j)
In [6]:
z1-z2
Out[6]:
(1+3j)
In [7]:
np.real(z1)
Out[7]:
4.0
In [8]:
np.imag(z1)
Out[8]:
5.0
In [9]:
w = np.complex(2,4)
z = np.complex(5,6)

realsum = np.real(w) + np.real(z)
imagsum = np.imag(w) + np.imag(z)
print(realsum, imagsum)

wPlusZ_separate = np.complex(realsum,imagsum)
wPlusZ_direct = w+z

print(wPlusZ_separate)
print(wPlusZ_direct)

7.0 10.0
(7+10j)
(7+10j)