Question

Simplify i^41. (2 points) i −1 −i 1

Answer 1

i

I got this right on the test!!

Answer 2

`\large\boxed{i^(41)=i}`

Explanation:

`i=√(-1)\\\\i^2=-1\\\\(-1)^2=1\\\\\text{Use}\ a^n\cdot a^m=a^(n+m)\ \text{and}\ (a^n)^m=a^(nm):\\\\i^(41)=i^(40+1)=i^(40)\cdot i=i^(2\cdot20)\cdot i=(i^2)^(20)\cdot i=(-1)^(20)\cdot i=1\cdot i=i`