Power Reduction Rule

Reference > Algebra: Imaginary Numbers

Description

The Power Reduction Rule states that:

\({i}^{n}={i}^{n\text{ mod }{4}}\)
Examples
\[{i}^{62}\]
1
Use Power Reduction Rule: \({i}^{n}={i}^{n\text{ mod }{4}}\)
In this case: \({\imath }^{62}={\imath }^{15\times 4+2}={\imath }^{2}\)
\[{\imath }^{2}\]

2
Use Square Rule: \({i}^{2}=-1\)
\[-1\]

Done