Exercise 1.5.1 (Order of each of the elements in $Q_8$)

Question

Compute the order of each of the elements in $Q_8$.

Richard Ganaye · Accepted Answer

\begin{proof} 
$Q_8 =\{1, -1,i,-i,j,-j,k,-k\}$.
We give the order of each element in $Q_8$:

\begin{center}
\begin{tabular}{|c|c|}
\hline
$x$ & $|x|$     \
\hline
1& 1 \
-1& 2\
i& 4\ 
-i& 4\
j& 4\
-j&4\
k& 4\
-k&4\
\hline
\end{tabular}
\end{center}
For instance, $i^2= -1 
e 0$, and $i^4 = (-1)^2 = 1$, so $|i| = 4$.
\end{proof}

Exercise 1.5.1 (Order of each of the elements in $Q_8$)

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Exercise 1.5.1 (Order of each of the elements in $Q_8$)

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