Answered

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simplify the given expression: 2/2+5i

Sagot :

IsrarAwan

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


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