Question

Simplify i 41

A) i
B)-1
C)-i
D) 1

Answer 1

Answer: The right option is A) i^41 = i

Explanation:

We want to simplify the expresion i^41.

now we will use the next relations:

a^(x*y) = (a^x)^y

(a^x)(a^y) = a^(a+y)

And we know tath i^2 = -1

i^3 = i*i^2 = -i

i^4 = (i^2)*(i^2) = -1*-1 = 1

now, i^41 = ((i^4)^10)*i = (1^10)*i = i

Answer 2

i^41 = (i^4)^((10) + 1) = i [i^4 = 1]