Question

What is the simplified form of i^14

Answer 1

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

Answer 2

I^14
=((i^2)^7)                  i^2=-1
=(-1)^7
=-1