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 :
[tex]P=i^{32}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
the value of the imaginary number i(iota) is given by
[tex]i=\sqrt{-1}~~~~~\Rightarrow i^2=-1.[/tex]
From expression (i), we get
[tex]P\\\\=i^{32}\\\\=(i^2)^{16}\\\\=(-1)^{16}\\\\=(1)^8\\\\=1.[/tex]
Thus, the required value of the given power of i is 1.
