Power of i

The alphabet i is referred to as the iota and is helpful to represent the imaginary part of the complex number. Further the iota(i) is very helpful to find the square root of negative numbers. We have the value of i² = -1, and this is used to find the value of √-4 = √i²4 = +2i  The value of i² = -1 is the fundamental aspect of a complex number. Let us try and understand more about the increasing powers of i.

• i = √-1
• i² = -1
• i³  = i.i² = i(-1) = -i
• i⁴ = (i²)² = (-1)² = 1
• i⁴ⁿ = 1
• i^{4n + 1} = i
• i^{4n + 2} = -1
• i^{4n + 3} = -i