Question

If i = √-1, then how many values does i^-2n have for different n ϵ Z?
1. One 
2. Two
3. Four
4. Infinite

Answer 1

Correct Answer - Option 2 : Two

Concept:

The value i or the concept of i is used in explaining and expressing complex numbers. Complex numbers are numbers with a real and imaginary part. The imaginary part is defined with the help of i. Basically, “i” is the imaginary part which is also called iota.

Value of i is √-1 A negative value inside a square root signifies an imaginary value. All the basic arithmetic operators are applicable to imaginary numbers. On squaring an imaginary number, we obtain a negative value.

i² = -1, i³ = -i, i⁴ = 1

Calculation:

Given

i = √-1

⇒ i² = -1

⇒ i-2n 

⇒ (i²)^-n

⇒ (-1)^-n

Since, n = 0, 1, 2, 3, ...

When n = even then i^-2n = 1

When n = odd then i-2n = -1

∴ Total possible values of the i-2n for n ϵ Z is two which are - 1 and 1.