Question

Simplify each of the following powers of i. i^32

Answer 1

the answer is 1. the trick here is to divide the exponent to 4.

Explanation:

i^32 32÷4=8

i

-1

-i

1

Answer 2

Answer: The required value of the given power of i is 1.

Step-by-step explanation: We are given to simplify the following power of i :

`P=i^(32)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We know that

the value of the imaginary number i(iota) is given by

`i=√(-1)~~~~~\Rightarrow i^2=-1.`

From expression (i), we get

`P\\\\=i^(32)\\\\=(i^2)^(16)\\\\=(-1)^(16)\\\\=(1)^8\\\\=1.`

Thus, the required value of the given power of i is 1.