Definition: Multiplication of complex numbers

Given two complex numbers \$z_1=a+bi\$ and \$z_2 = c+di\$, where a,b,c, and d are real numbers and i is the imaginary unit with \$ i^2 = −1\$, their product is:
\$ z_1 * z_2 = (a+bi)(c+di) = (ac−bd)+(ad+bc)i \$

This definition extends the distributive property of multiplication to complex numbers and accounts for the fundamental property of the imaginary unit i.