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Kernel: Unknown Kernel
import math
math.sqrt(-1)
math.asin(5)
--------------------------------------------------------------------------- ValueError Traceback (most recent call last) <ipython-input-5-0d68b6ad17b4> in <module>() 1 import math ----> 2 math.sqrt(-1) 3 math.asin(5) ValueError: math domain error 
from cmath import sqrt
sqrt(-1)
sqrt(1j)

sqrt(5)

sqrt(1j)

from cmath import *

exp(pi*1j)

log(-5)

cos(1j)
(1.5430806348152437-0j)
a=2
b=3
c=a + b*1j
print(c)
print(c.real)
print(c.imag)
print(c.conjugate())
c**(2)
(2+3j) 2.0 3.0 (2-3j)
(-5+12j)
sqrt(4)
(2+0j)
from numpy.lib.scimath import *

print(sqrt(4))
print(sqrt(-4))
2.0 2j 
a=1
b=0
c=-4
x1 = (-b + sqrt(b**2 - 4*a*c))/(2*a)
x2 = (-b - sqrt(b**2 - 4*a*c))/(2*a)
print('The roots of %gx^2 + %gx + %g are ' % (a,b,c) + str(x1) + ' and ' +  str(x2) + '.')
The roots of 1x^2 + 0x + -4 are 2.0 and -2.0. 
arccos(0.5)
1.0471975511965979
from sympy import symbols, diff, sqrt, integrate, Rational, lambdify, exp, limit
a, b, c, t =  symbols('a b c t')
y = (-b + sqrt(b**2 - 4*a*c))/(2*a)
z = t**3 + 2*exp(t)

dyda = diff(y, a)
dyda
dzdt = diff(z,t)
dzdt
3*t**2 + 2*exp(t)
Y = integrate(dzdt,t)
Y
t**3 + 2*exp(t)
quad = lambdify([a, b, c], y)
quad(1, 2, -3)
zfunc = lambdify([t],z)
zfunc(3)
67.17107384637534
from sympy import simplify, expand, sin, cos
z = (a+b)**5
z2 = expand(z)
z2
a**5 + 5*a**4*b + 10*a**3*b**2 + 10*a**2*b**3 + 5*a*b**4 + b**5
f = sin(a)*cos(b)+sin(b)*cos(a)
f2 = simplify(f)
f2
sin(a + b)
f = sin(t)/t
f.series(t,0,15)
1 - t**2/6 + t**4/120 - t**6/5040 + t**8/362880 - t**10/39916800 + t**12/6227020800 - t**14/1307674368000 + O(t**15)