Complex Numbers in Polar Form | Modulus-Argument Form

This video explains the modulus-argument form of complex numbers and demonstrates how to convert a complex number from its general form (z = x + iy) to modulus-argument form.

I show that the real part (x) can be expressed as r cos θ, and the imaginary part (y) as r sin θ, where r is the modulus and θ is the argument of the complex number. Substituting these into z = x + iy yields the modulus-argument form: z = r(cos θ + i sin θ).

I then work through four examples, converting each to modulus-argument form by calculating their respective moduli and arguments. These examples are chosen to represent complex numbers located in each of the four quadrants of the Argand diagram.