what is the value of $i^{20 + 1}$?\n1\n-1\n$-i$\ni

Explanation:

Step1: Recall the powers of $i$

The powers of the imaginary unit $i$ follow a cycle: $i^1 = i$, $i^2=- 1$, $i^3 = i^2\times i=-i$, $i^4=(i^2)^2 = 1$.

Step2: Simplify the exponent

We first simplify the exponent of $i$. Since $20\div4 = 5$ with a remainder of $0$, $i^{20}=(i^4)^5$. Since $i^4 = 1$, then $(i^4)^5=1^5 = 1$.

Step3: Calculate $i^{20 + 1}$

We know that $i^{20+1}=i^{20}\times i$. Since $i^{20}=1$, then $i^{20}\times i=1\times i = i$.

Answer:

$i$