What is the value of i⁹⁷ - i?

Solution:

We know that

i² = √-1 × √-1

= √(-1 × -1)

= 1(1)

i⁹⁷ - i

= i⁹⁶i - i

= (i²)⁴⁸ . i - i

From (1) we know i² = 1,

Therefore

= (1)⁴⁸.i - i

= 1.i - i

= i - i

= 0

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What is the value of i⁹⁷ - i?

Summary:

The value of i⁹⁷ - i is zero.