Which expression is equivalent to i²³³?
1, -1, i, -i

Solution:

Given i233

We know that i² = -1 , if we square (i²) we get (-1)² = 1

So, if i is multiplied to (i²), we get i³ = (-1).i = -i

Again if i is multiplied to i³ , we get i⁴ = (-i).i = -i² = -(-1) = 1

Hence, all even powers of i after 2, will give answer as 1

The sequence will continue as a cycle as i, -1, -i, 1

So, i²³³ can be rewritten as i^{232 + 1}= i²³².i

i233 = (i²)¹¹⁶ .i = (-1)¹¹⁶ . i

Since the power 116 is even , the term becomes 1.i = i

Therefore, i²³³ = i

Which expression is equivalent to i²³³?

Summary:

i is expression is equivalent to i²³³.