The answer is the option d, which is: d) [tex] \frac{-77+21i}{130} [/tex]
The explanation for this problem is shown below:
1. Smplify the denominator and rewrite the numerator in this form:
[tex] \frac{7i}{7-2i-4-9i} \\\frac{7i}{3-11i} [/tex]
2. Multiply the denominator and the numerator by the conjugated [tex] (3+11i) [/tex] and simplify the expression, as following:
[tex] \frac{7i(3+11i)}{(3-11i)(3+11i)} \\ \frac{21i+77i^{2}}{121+9} \\ \frac{-77+21i}{130} [/tex]
3. As you can see, you obtain the expression shown in the option mentioned above.
