(i)
(ii)
(iii)
(iv)
(v)
Power of
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.,
Example:
Let
Conjugate of a Complex Number
Let , be a complex number. Then, the complex conjugate of
, denoted by
, is a complex number
, i.e.,
.
Example:
If
NOTE:
(i) Let , be a complex number which is purely real, it has no imaginary part.
i.e.,
(ii) Let , be a complex number which is called purely imaginary, it have no real part.
i.e,
Some Important Properties:
(i) If then we get,