Statement:
for any integer
.
De-Moivre’s Theorem (for Rational Index)
Let be two integers with
,
Example 1:
Example 2:
Solve:
Principal Argument of in the interval
(i) In the interval
(ii) In the interval
(iii) In the interval
(iv) In the interval
All of the angles () in the interval
are in anti-clockwise direction.
Principal Argument of in the interval (-\pi < \theta \leq \pi)
(i) In the interval
(ii) In the interval
All of the angles in the interval are in clockwise direction.