The correct answer is: \(\frac{4-10i}{29}\)
Explanation:
Given expression:
\(\frac{2}{2+5i}\)
Apply rationalization (multiply and divide by (2-5i)):
\(\frac{2}{2+5i} * (\frac{2-5i}{2-5i} )\)
Now evalute as follows:
\(\frac{4-10i}{(2)^2-(5i)^2}\)
Remember \(i^2 = -1\)
\(\frac{4-10i}{4-(-25)} \\ \frac{4-10i}{29}\)
Hence the correct answer is \(\frac{4-10i}{29}\).
-i
