How Do You Simplify the Square of Complex Conjugates?

[charmedbeauty]

Homework Statement

Simplify ($\sqrt{3+4i}$+$\sqrt{3-4i}$)$^{2}$

Homework Equations

The Attempt at a Solution

well I tried expanding it out but I don't think that is the right approach but I have no other idea to tackle the problem?

so by expanding I had 6+2($\sqrt{3+4i}$)($\sqrt{3-4i}$)

But then I didnt know where to go

please help!

 

[The1337gamer]

$$(\sqrt{3+4i})(\sqrt{3-4i})=\sqrt{(3+4i)(3-4i)}$$

Now how can you simplify the term in the sqrt? Notice we have a complex number multiplied by it's complex conjugate