Python for Basic problems in Complex Numbers

Introduces complex numbers as the sum of real and imaginary parts, uses G as the imaginary unit, and explains magnitude as distance on the complex plane and rotation by G.

Learn to create complex numbers in Python by direct notation, the 1j form, and the complex() function; plot them on a Matplotlib complex plane and extract real and imaginary parts.

Explore addition, subtraction, and multiplication of complex numbers, combining real and imaginary parts with a concrete example that results in -1 plus 31i.

Use the complex conjugate of the denominator to divide a complex number, multiply numerator and denominator by the conjugate, and apply the difference of squares to simplify.

Learn to perform mathematical operations on complex numbers in Python, including addition, subtraction, multiplication, and division, and compute the complex conjugate with Python.

Calculate the magnitude and phase of a complex number using sqrt(re^2 + im^2) and arctan(im/re); for 5+6i, magnitude is sqrt(61) and the phase is arctan(6/5).

Compute the magnitude and phase of a complex number in python using the real and imaginary parts, then convert the phase to degrees for interpretation.

Generate a complex sine wave in Python by defining simulation parameters and 100 linearly spaced samples from 0 to 10 seconds at 50 hertz, then plot real and imaginary parts.