Question

\[\sqrt{-64} / (7 - 6i) - (2 - 2i)\]

Answer 1

not clear where the minus sign is. is this
\[\frac{\sqrt{-64}}{7-6i}-(2-2i)\]?

Answer 2

no it is (7 - 6i) - (2 -2i)... that is underneath the fraction bar so the \[\sqrt{-64}\] is on top.

Answer 3

ok so
\[(7-6i)-(2-2i)=5-4i\] and
\[\sqrt{-64}=8i\] so your real problem is
\[\frac{8i}{5-4i}\]

Answer 4

multiply numerator and denominator by the "conjugate" of the denominator, namely
\[5+4i\] and it is always true that
\[(a+bi)(a-bi)=a^2+b^2\] so your denonimator will be
\[5^2+4^2=41\]

Answer 5

in other words you have
\[\frac{8i}{5-4i}\times \frac{5+4i}{5+4i}=\frac{8i(5+4i)}{41}\] and now multiply out in the numerator

Answer 6

so the answer would be 32 + 40i/ 41?