Plotting Complex Numbers

Complex numbers can be plotted on a special graph called the complex plane. The horizontal axis shows the real part, and the vertical axis shows the imaginary part.

Modulus and Argument

• Modulus: The distance from the origin, calculated as \(|z| = \sqrt{a^2 + b^2}\) for \(z = a + bi\).
• Argument: The angle from the positive real axis to the point representing \(z\).

Polar Form

Any complex number \(z = a + bi\) can also be written as \(z = r(\cos \theta + i\sin \theta)\), where \(r\) is the modulus and \(\theta\) is the argument.

Why Polar Form?

Polar form is super helpful for multiplying and dividing complex numbers, especially in engineering and signal processing.