In general, for any ,
Here, are roots of the equation , where we get two real roots, and and two imaginary roots and , by solving:
The Modulus of a Complex Number
Let be a complex number. Then, the modulus of , denoted by , is defined to be the non-negative real number i.e.,
Conjugate of a Complex Number
Let , be a complex number. Then, the complex conjugate of , denoted by , is a complex number , i.e., .
(i) Let , be a complex number which is purely real, it has no imaginary part.
(ii) Let , be a complex number which is called purely imaginary, it have no real part.
Some Important Properties:
(i) If then we get,