Complex numbers allow us to solve equations for which no real solution can be found. Consider, for example, the equation
which cannot be satisfied for any real number. By introducing an imaginary unit1 so that j2 = −1, Eqn. (A.1) can be solved to yield
Similarly, the equation
has the solutions
A general complex number is in the form
where a and b are real numbers. The values a and b are referred to as the real part and imaginary part of the complex number x respectively. Following notation is used for real and imaginary parts of a complex number:
For two complex numbers to be equal, both their real ...