Need Help 19th question

[Sleeplesscoot]

19th question

 

[Romsek]

can you compute \(\displaystyle i^n,~n \in \mathbb{Z}\) ?

you'll find the values repeat after a bit

 

[Sleeplesscoot]

Yes They are repeating

 

[Deleted member 4993]

Yes They are repeating

What repeat sequence do you see?

So how can you use that fact here?

 

[Sleeplesscoot]

I see this sequence -1,-i,1,i.....

 

[pka]

View attachment 1510419th question

Sleeplesscoot, If you know how to use the modulo function that will help here.
Look HERE you can "play'' with various numbers. Then all you need to learn is \(\displaystyle i^1=i,~i^2=-1,~i^3=-i,~\&~i^4=1\).

 

[Sleeplesscoot]

Can you solve it for me? I am not really getting it

 

[Deleted member 4993]

Can you solve it for me? I am not really getting it

What is the problem asking for?

Can you please REWRITE that here?

In addition, write the first 8 elements of the sequence S_n (= i ⁿ + i)

 

[pka]

Can you solve it for me? I am not really getting it

\(\displaystyle S(n)=\)\(\displaystyle \left\{ \begin{gathered}
1 + i,n \equiv 0\bmod 4 \hfill \\
2i,n \equiv 1\bmod 4 \hfill \\
- 1 + i,n \equiv 2\bmod 4 \hfill \\
0,n \equiv 3\bmod 4 \hfill \\
\end{gathered} \right.\)________________ SEE HERE

 

[Sleeplesscoot]

I get it now thanks