Question

I need help with simplifying this fraction!

Answer 1

$\bf \stackrel{\textit{let's recall that}}{i^2=-1\qquad \qquad i^4=1} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{3}{i^{23}}\implies \cfrac{3}{i^{20+2+1}}\implies \cfrac{3}{i^{20}i^2 i}\implies \cfrac{3}{i^{4\cdot 5}i^2 i}\implies \cfrac{3}{(i^4)^5 i^2 i}\implies \cfrac{3}{(1)^5(-1)i} \\\\\\ \cfrac{3}{-i}~\hspace{7em}\stackrel{\textit{and if we rationalize the denominator}}{\cfrac{3}{-i}\cdot \cfrac{i}{i}\implies \cfrac{3i}{-i^2}\implies \cfrac{3i}{-(-1)}}\implies 3i$