Answer
$-\dfrac{7}{74}-\dfrac{5}{74}i$
Work Step by Step
Multiplying the numerator and the denominator by the conjugate of the denominator, the given expression, $
\dfrac{-1}{7-5i}
,$ is equivalent to
\begin{align*}\require {cancel}
&
\dfrac{-1}{7-5i}\cdot\dfrac{7+5i}{7+5i}
\\\\&=
\dfrac{-1(7+5i)}{7^2-(5i)^2}
&\left( \text{use }(a+b)(a-b)=a^2-b^2 \right)
\\\\&=
\dfrac{-1(7+5i)}{49-25i^2}
\\\\&=
\dfrac{-7-5i}{49-25i^2}
&\left( \text{use Distributive Property } \right)
\\\\&=
\dfrac{-7-5i}{49-25(-1)}
&\left( \text{use }i^2=-1 \right)
\\\\&=
\dfrac{-7-5i}{49+25}
\\\\&=
\dfrac{-7-5i}{74}
\\\\&=
-\dfrac{7}{74}-\dfrac{5}{74}i
.\end{align*}
Hence, in the form $a\pm bi,$ the given expression is equivalent to $
-\dfrac{7}{74}-\dfrac{5}{74}i
$.
