## ABSTRACT

We begin by briefly reviewing complex numbers and their properties. In Section 2.1, we defined a number z to be complex if z = x + iy, where x and y are

real and i √−1. Given a complex number z = x + iy, where x and y are real, we call

x the real part of z and write x = Re(z), and we call y the imaginary part of z and write y = Im(z). Both Re(z) and Im(z) are real numbers. If Re(z) = 0, we say z is imaginary; if Im(z) = 0, we say z is real. From now on, if we write a > 0 or say that “a is positive,” then we are implicitly assuming that a is real. Given a complex number z = x + iy, where x and y are real, we denote z = x − iy and

call it the complex conjugate of z. We have that

Re(z) = z+ z 2

and Im(z) = z− z 2i

.