Find the value

Question

i²⁴+i^-26

Answer 1

Here is something that will help you solve these problems:

 

i¹ = i

i² = -1

i³ = -i

i⁴ = 1

 

To find iⁿ, look at whether n is a multiple of 4, or has a remainder of 1, 2, or 3.

 

n = 4k + 1 ⇒ iⁿ = i

n = 4k + 2 ⇒ iⁿ = -1

n = 4k + 3 ⇒ iⁿ = -i

n = 4k  ⇒ iⁿ = 1

 

i²⁴ = i⁴⁽⁶⁾ = 1

 

i^-26 = 1/i²⁶ = 1/i⁴⁽⁶⁾⁺² = 1/-1 = -1

 

⇒

 

i²⁴ + i^-26 = 1 - 1 = 0