Generate a monic polynomial with given complex roots in Python

To generate a monic polynomial with given complex roots, use the polynomial.polyfromroots() method in Python Numpy. The method returns the 1-D array of the polynomial’s coefficients If all the roots are real, then out is also real, otherwise it is complex. The parameter roots are the sequence containing the roots.

Steps

At first, import the required libraries -

from numpy.polynomial import polynomial as P

Given complex roots −

j = complex(0,1)
print("Result...\n",P.polyfromroots((-j,j)))

Get the datatype −

print("\nType...\n",P.polyfromroots((-j, j)).dtype)

Get the shape −

print("\nShape...\n",P.polyfromroots((-j, j)).shape)

Example

from numpy.polynomial import polynomial as P

# To generate a monic polynomial with given roots, use the polynomial.polyfromroots() method in Python Numpy.

# The method returns the 1-D array of the polynomial’s coefficients If all the roots are real, then out is also real, otherwise it is complex.

# The parameter roots are the sequence containing the roots.
j = complex(0,1)
print("Result...\n",P.polyfromroots((-j,j)))

# Get the datatype
print("\nType...\n",P.polyfromroots((-j, j)).dtype)

# Get the shape
print("\nShape...\n",P.polyfromroots((-j, j)).shape)

Output

Result...
[1.+0.j 0.+0.j 1.+0.j]

Type...
complex128

Shape...
(3,)