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