Complex Numbers

This section reviews basic operations with complex numbers ($a+bi$).

• Multiplication: $(a+bi)(c+di) = (ac-bd) + (ad+bc)i$.
• Rationalization (Inverse): $(a+bi)^{-1} = \frac{a-bi}{a^2+b^2}$.
• Modulus: $|a+bi| = \sqrt{a^2+b^2}$.

For example, $(3-2i)(4+i) = (3 \cdot 4 - (-2) \cdot 1) + (3 \cdot 1 + (-2) \cdot 4)i = 14 - 5i$.