Question

What is the value of i 20+1?
1
–1
–i
i

Answer 1

I got 2 but thats not an option?

Answer 2

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

Answer 3

yes!
sorry

Answer 4

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.

Answer 5

Anyway,

Answer 6

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

Answer 7

oh duh, answer is i

Answer 8

yes, that is 1.

Answer 9

So,

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

Answer 10

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)

Answer 11

(saying, for any whole number n)

Answer 12

If you got any questions, please ask...