Imaginary Numbers in Python

import numpy as np
import matplotlib.pyplot as plt

# Complex vector example
a = 1 + 1j

def complexCalc(complexNum):
    """ Returns the Real, imaginary, phase and magnitude of a complex number
    
    Parameters
    ----------
    complexNum: Complex number 
    
    Returns
    ----------
    Ra: Real Part
    Ima: Imaginary Part 
    phia: Angle in Radians 
    maga: Magnitude
 """
    
    # Real and imaginary parts
    Ra = complexNum.real 
    Ima = complexNum.imag 
    # Phase of the complex vector, in radians (pi radians = 180 degree)
    phia = np.angle(complexNum)
    # Magnitude of the complex vector
    maga = np.abs(complexNum)
    print("The Vector", complexNum)
    print("Real:",Ra )
    print("Imaginary:", Ima)
    print("Phase:", (180/np.pi)*phia, "degree")
    print("Magnitude:", maga)
    return Ra, Ima, phia, maga

Ra, Ima, phia, maga = complexCalc(a)

# Converting from polar to rectangular
a = 1 + 1j
Ra, Ima, phia, maga = complexCalc(a)
# Calculate real and imaginary parts
Ra = maga * np.cos(phia)
Ima = maga * np.sin(phia)

# Combine into a complex number
aRect = Ra + 1j * Ima

print("--- Back to Rectangular ---")
Ra, Ima, phia, maga = complexCalc(aRect)

# Create a new figure with a polar subplot
fig, ax = plt.subplots(figsize=(8, 8), subplot_kw={'projection': 'polar'})

# Plot vector a in blue
ax.plot(
    [0, phia],  # Angles from 0 to angle of a
    [0, maga],    # Magnitude from 0 to magnitude of a
    marker='o',        # Marker at the end
    color='b',         # Color blue
    label=f'Vector {a}'
)

# Customize angular ticks: Only degrees
ax.set_xticks([0, np.pi/2, np.pi, 3*np.pi/2])  # Set 0°, 90°, 180°, 270°
ax.set_xticklabels(['0°', '90°', '180°', '270°'], fontsize=12)
ax.set_yticks([])
ax.legend(loc='upper right', bbox_to_anchor=(1.1, 1.1))

# Add axis labels
r_max = maga * 1.2  # Extend radius for label positioning
ax.text(0, r_max, 'Real', fontsize=14, ha='center', va='bottom')            # X-axis (Real)
ax.text(np.pi/2, r_max, 'Imaginary', fontsize=14, ha='center', va='bottom') # Y-axis (Imaginary)

# Enable Grid for better readability
ax.grid(True)

# Title for the plot
fig.suptitle('Visualize the Imaginary Vectors', y=0.05, fontsize=14, va='top')

plt.show()

a = 1 + 1j
b = 0 + 1j

Ra, Ima, phia, maga = complexCalc(a)
Rb, Imb, phib, magb = complexCalc(b)

# Create a new figure with a polar subplot
fig, ax = plt.subplots(figsize=(8, 8), subplot_kw={'projection': 'polar'})

# Plot vector a in blue
ax.plot(
    [0, phia],  # Angles from 0 to angle of a
    [0, maga],    # Mag from 0 to magnitude of a
    marker='o',        # Marker at the end
    color='b',         # Color blue
    label=f'Vector {a}'
)

# Customize angular ticks: Only degrees
ax.set_xticks([0, np.pi/2, np.pi, 3*np.pi/2])  # Set 0°, 90°, 180°, 270°
ax.set_xticklabels(['0°', '90°', '180°', '270°'], fontsize=12)
ax.set_yticks([])
ax.legend(loc='upper right', bbox_to_anchor=(1.1, 1.1))

# Add axis labels
r_max = np.abs(a) * 1.2  # Extend radius for label positioning
ax.text(0, r_max, 'Real', fontsize=14, ha='center', va='bottom')            # X-axis (Real)
ax.text(np.pi/2, r_max, 'Imaginary', fontsize=14, ha='center', va='bottom') # Y-axis (Imaginary)

# Enable Grid for better readability
ax.grid(True)

# Title for the plot
fig.suptitle('Visualize the Imaginary Vectors', y=0.05, fontsize=14, va='top')

plt.show()

# Create a new figure with a polar subplot
fig, ax = plt.subplots(figsize=(8, 8), subplot_kw={'projection': 'polar'})

# Plot vector a in blue
ax.plot(
    [0, phia],  # Angles from 0 to angle of a
    [0, maga],    # Radii from 0 to magnitude of a
    marker='o',        # Marker at the end
    color='b',         # Color blue
    label=f'Vector {a}'
)
ax.plot(
    [0, phib],  # Angles from 0 to angle of a
    [0, magb],    # Mag from 0 to magnitude of a
    marker='o',        # Marker at the end
    color='g',         # Color blue
    label=f'Vector {b}'
)

# Customize angular ticks: Only degrees
ax.set_xticks([0, np.pi/2, np.pi, 3*np.pi/2])  # Set 0°, 90°, 180°, 270°
ax.set_xticklabels(['0°', '90°', '180°', '270°'], fontsize=12)
ax.set_yticks([])
ax.legend(loc='upper right', bbox_to_anchor=(1.1, 1.1))

# Add axis labels
rmax = np.abs(a) * 1.2  # Extend radius for label positioning
ax.text(0, rmax, 'Real', fontsize=14, ha='center', va='bottom')            # X-axis (Real)
ax.text(np.pi/2, rmax, 'Imaginary', fontsize=14, ha='center', va='bottom') # Y-axis (Imaginary)

# Enable Grid for better readability
ax.grid(True)

# Title for the plot
fig.suptitle('Visualize the Imaginary Vectors', y=0.05, fontsize=14, va='top')

plt.show()

complexArr = np.array([1 + 1j, 1 - 1j, 4 - 3j, 2 + 4j])
complexUnpacked = np.zeros((4,4))

def visualIzeComplexNums(complexArr):
    """ Plots an array of complex numbers
    
    Parameters
    ----------
    complexArr: Array of complex numbers
    
    Uses a matrix complexUnpacked to store the extracted values
  """
    # Check for array
    if (isinstance(complexArr, list) or isinstance(complexArr, np.ndarray)):
        complexUnpacked = np.zeros((len(complexArr),4))
        # complexUnpacked is a matrix -> [0, (0,1,2,3)] = Ra, Ima, phia, maga
    else:
        print("Not an array of complex numbers")
        return 0
    
    # Iterate through each array index
    for arrInd, arr in enumerate(complexArr):
        complexUnpacked[arrInd,0],complexUnpacked[arrInd,1],complexUnpacked[arrInd,2],complexUnpacked[arrInd,3] = complexCalc(arr) 


    # Create a new figure with a polar subplot
    fig, ax = plt.subplots(figsize=(8, 8), subplot_kw={'projection': 'polar'})
    cmap = plt.cm.get_cmap('tab10', len(complexArr)) 
    colors = [cmap(i) for i in range(len(complexArr))]

    # Plot vectors
    for arrInd, arr in enumerate(complexArr):
        ax.plot([0, complexUnpacked[arrInd,2]],[0, complexUnpacked[arrInd,3]],marker='o',color=colors[arrInd],label=f'Vector {arr}')


    # Customize angular ticks: Only degrees
    ax.set_xticks([0, np.pi/2, np.pi, 3*np.pi/2])  # Set 0°, 90°, 180°, 270°
    ax.set_xticklabels(['0°', '90°', '180°', '270°'], fontsize=12)
    ax.set_yticks([])
    ax.legend(loc='upper right', bbox_to_anchor=(1.1, 1.1))

    # Add axis labels
    rmax = np.abs(a) * 1.2  # Extend radius for label positioning
    ax.text(0, rmax, 'Real', fontsize=14, ha='center', va='bottom')            # X-axis (Real)
    ax.text(np.pi/2, rmax, 'Imaginary', fontsize=14, ha='center', va='bottom') # Y-axis (Imaginary)

    # Enable Grid for better readability
    ax.grid(True)

    # Title for the plot
    fig.suptitle('Visualize the Imaginary Vectors', y=0.05, fontsize=14, va='top')

    plt.show()
    
# Calling the function
visualIzeComplexNums(complexArr)

a = 2+ 4j
# Rotate by 90 degrees
rota = 1j * a
print(rota)

complexArr = [a, rota]
visualIzeComplexNums(complexArr)

a = 2+4j
aconj = np.conj(a)

complexArr = [a, aconj]
visualIzeComplexNums(complexArr)

# Arithmetic
a = 1+ 0.5j
b = 0 + 0.5j
# Sum
z = a + b
print(z)
complexArr = [a, b, z]
visualIzeComplexNums(complexArr)

# Multiplication
z = a*b
print(z)
complexArr = [a, b, z]
visualIzeComplexNums(complexArr)

# Multiplication in polar 
# Addition of the phase and multiplication of the magnitude

a = 1+ 0.5j
b = 0 + 0.5j

Ra, Ima, phia, maga = complexCalc(a)
Rb, Imb, phib, magb = complexCalc(b)

magz = maga * magb
phiz = phia + phib

# Converting from polar to rectangular

# Calculate real and imaginary parts
Rz = magz * np.cos(phiz)
Imz = magz * np.sin(phiz)

# Combine into a complex number
z = Rz + 1j * Imz
complexArr = [a, b, z]
visualIzeComplexNums(complexArr)

# Complex Division
z = a/b
print(z)
complexArr = [a, b, z]
visualIzeComplexNums(complexArr)

# Division in polar 
# Subtraction of the phase and division of the magnitude



a = 1+ 0.5j
b = 0 + 0.5j

Ra, Ima, phia, maga = complexCalc(a)
Rb, Imb, phib, magb = complexCalc(b)

magz = maga / magb
phiz = phia - phib

# Converting from polar to rectangular

# Calculate real and imaginary parts
Rz = magz * np.cos(phiz)
Imz = magz * np.sin(phiz)

# Combine into a complex number
z = Rz + 1j * Imz
complexArr = [a, b, z]
visualIzeComplexNums(complexArr)