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Question

Help?

adrianna.gongora · Answer

$$\frac{ 2 }{ 2+5i }$$

greatlife44 · Answer

Hm.. you want to rationalize this?

mathmusician · Answer

you want to move the 5i to the other side of the fraction

adrianna.gongora · Answer

It says to simplify the given expression.

mathmusician · Answer

you do that by multiplying both the numerator and the denominator by 2+5i

greatlife44 · Answer

I'm wondering if this could be a step 

@mathmusician 

$$\frac{ 2 }{ 2+5i }*(\frac{ 2-5i }{ 2-5i })$$

greatlife44 · Answer

$$i = \sqrt{-1}$$

greatlife44 · Answer

$$i^{2} = (\sqrt{-1})^{2} = -1$$

adrianna.gongora · Answer

Here this is the question and the answer choices.

mathmusician · Answer

Yes that is a a step @greatlife44

adrianna.gongora · Answer

It's the last question I have and I'm just stuck on it

greatlife44 · Answer

I'm wondering if this could be a step 

@mathmusician 

$$\frac{ 2 }{ 2+5i }*(\frac{ 2-5i }{ 2-5i })$$


$$(2+5i)(2-5i) = (4-25i^{2})$$

remember if we apply the fact that i^{-2} = -1 we can simplify our denominator. 

$$i^{2} = -1$$

4-25(-1) 

4-(-25) = 29 

$$\frac{ 4-10i }{ 29 }$$

adrianna.gongora · Answer

How did you get the 4-10i ?

adrianna.gongora · Answer

Never mind I see it

adrianna.gongora · Answer

Thank you both so much I didn't even know what to do. I was completely stuck on it.

greatlife44 · Answer

@Adrianna.Gongora


the idea is to get i out of the denominator.