## anonymous one year ago What is the value of i 20+1? 1 –1 –i i

1. anonymous

I got 2 but thats not an option?

2. SolomonZelman

maybe you meant $$\large\color{black}{ \displaystyle i^{20+1} }$$ ?

3. anonymous

yes! sorry

4. SolomonZelman

yes, it is alright. next when you want to write that, just say i^(20+1) where ^ indicates an exponent, and (...) tell you what your exponent is.

5. SolomonZelman

Anyway,

6. SolomonZelman

Can you tell me what does $$\large\color{black}{ \displaystyle i^4 }$$ equal to?

7. anonymous

8. SolomonZelman

yes, that is 1.

9. SolomonZelman

So, $$\large\color{black}{ \displaystyle i^{20+1}=i^{20} \times i^1=i^{4\times 5}\times i=\left(i^4\right)^5\times i = 1^5\times i=? }$$

10. SolomonZelman

well, you probably know anyway that $$\large\color{black}{ \displaystyle i^{4n}=1 }$$ $$\large\color{black}{ \displaystyle i^{4n+1}=i }$$ $$\large\color{black}{ \displaystyle i^{4n+2}=-1 }$$ $$\large\color{black}{ \displaystyle i^{4n+3}=-i }$$ and again restarting the cycle, $$\large\color{black}{ \displaystyle i^{4n+4}=1 }$$ and so on... (this is true for any whole number powers of i)

11. SolomonZelman

(saying, for any whole number n)

12. SolomonZelman