# Complex number Problem

Algebra

### Complex number Problem

Greetings , I was solving a list of practice exercises when I got to this question, and I quite can't understand what to do about it. Could you please help me?
this is the question

Being a a real number and the imagnary part of the complex number zero, so a is:

(2+i)/(a+2i)

a)-4
b)-4
c)1
d)2
e)4
I appreciate the time you took.
Thank you.
Learningforcomp

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### Re: Complex number Problem

Good afternoon!

$$\frac{2+i}{a+2i}=\frac{2+i}{a+2i}\cdot\frac{a-2i}{a-2i}\\ =\frac{(2+i)(a-2i)}{a^2+2^2}=\frac{2a-4i+ai+2}{a^2+4}\\ =\frac{2a+2+(a-4)i}{a^2+4}$$

Imaginary part is zero:
a=4

I hope to have helped!

Baltuilhe

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