Question

8i/(5-8i)

Answer 1

We can't have irrationals in the denominator, much less imaginaries! Multiply by the conjugate of the denominator.
\[\frac{8i}{5-8i}*\frac{5+8i}{5+8i}\]

Answer 2

\[8 \times \frac{ i }{ 5-8i } = 8 \frac{ i }{ 5-8i} \times \frac{ 5+8i }{ 5+81 }\]

Answer 3

\[\frac{(8i)(5+8i)}{(5-8i)(5+8i)}\]

Multiplying complex conjugates always simplifies from (a+bi)(a-bi) to (a^2+b^2). Your denominator, (5-8i)(5+8i), becomes 25+64, or 89.

The numerator, 8i(5+8i), can be easily distributed. 8i*5+8i*8i=40i+64i^2=40i-64.

\[\frac{-64+40i}{89}\] is what you should have now, unless I did something wrong. Otherwise, it doesn't appear to be further reducible.