Modulus and Argument of Complex Numbers

Complex numbers can be represented using their distance from the origin (modulus) and angle with the positive real axis (argument).

Modulus

Argument

Polar Form

Example: Converting to Polar Form

Converting from Polar to Rectangular

Argument in Different Quadrants

Multiplication in Polar Form

Example: Multiplying in Polar Form

Practice Problems

1. Find the modulus and argument of .
2. Write in polar form.
3. Convert to rectangular form.
4. Multiply and .