Question

If n is a positive integer, then which of the following relations is false

• A. $i^{4n}=1$
• B. $i^{4n-1}=i$
• C. $i^{4n+1}=i$
• D. $i^{4n+2}=-1$

Answer 1

The correct option is B $i^{4n-1}=i$

We know that $i^2=-1\Rightarrow (i^2{)}^2=(-1{)}^2=1\Rightarrow i^{4n}=1^n$ and therefore $i^{4n-1}=-i$