Complex Numbers

Let us denote √−1 by the symbol i. Then, we have 2 i = −1 . This means that i is a solution of the equation x² + 1 = 0. A number of the form a + ib, where a and b are real numbers, is defined to be a complex number.

For example, 2 + i3, (– 1) + i√ 3 are complex numbers. For the complex number z = a + ib, a is called the real part, denoted by Re z and b is called the imaginary part denoted by Im z of the complex number z. For example, if z = 2 + i5, then Re z = 2 and Im z = 5. Two complex numbers z 1 = a + ib and z 2 = c + id are equal if a = c and b = d.