Question

sqrt-64 / (7-6i) - (2-2i)

choices:
-64+40i/-3
64+40i/-3
-32+40i/41
32+40i/41

Answer 1

We have
\[\frac{\sqrt {-64}}{(7-6i-(2-2i))}\]
Now we know that \(\sqrt {-1}=i\)
so
\[\frac{\sqrt {64}\times \sqrt {-1}}{(7-6i-(2-2i))}\]
\[\frac{8i}{(7-6i-(2-2i))}\]
Let's simplify the denominator

\[\frac{8i}{(7-6i-2+2i)}\]
\[\frac{8i}{(5-4i)}\]
Let's multiply the numerator and denominator by 5+4i
\[\frac{8i}{(5-4i)}\times \frac{5+4i}{5+4i}\]
now we get
\[\frac{40i+32i^2}{25+16}\]
we get
\[\frac{-32+40i}{41}\]