A complex number is commonly written in the form
z = a + bi
here a is known as the real part of the number z, b be the imaginary part of z, and i is √-1 . This is the way mathematicians generally write a complex number; in engineering it is frequently written as a + bj, where j is √-1. A complex number is purely imaginary if it is of the form z = bi (in another words, if a is 0).