Answer:
\(i^{14}=-1\)
Step-by-step explanation:
The given expression is
\(i^{14}\)
We know that
\(i^4=1\)
Hence, on dividing 14 by 4 we get 3 as quotient and 2 as remainder. Hence, we can write the expressions as
\(i^{14}\\\\=(i^4)^3\cdot i^2\)
Now, use the values \(i^4=1,i^2=-1\)
\((i^4)^3\cdot i^2\\\\=1^3\cdot (-1)\\\\=-1\)
Therefore, the simplified form of the expression is -1
