Complex Numbers and Quadratic Equations

The symbol i is defined so

The symbol i is defined so that i^2 = -1. It is a solution of x^2 + 1 = 0. This makes it possible to work with square roots of negative numbers.

A complex number is any number

A complex number is any number of the form a + ib, where a and b are real numbers. Here, a is the real part and b is the imaginary part.

Two complex numbers z1 =

Two complex numbers z1 = a + ib and z2 = c + id are equal if and only if a = c and b = d.

If z1 = a + ib

If z1 = a + ib and z2 = c + id, then z1 + z2 = (a + c) + i(b + d). Subtraction is defined as z1 - z2 = z1 + (-z2).

If z1 = a + ib

If z1 = a + ib and z2 = c + id, then z1z2 = (ac - bd) + i(ad + bc). Multiplication is closed, commutative, associative, and distributive over addition