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