How Do You Simplify the Square of Complex Conjugates?

AI Thread Summary
To simplify (\sqrt{3+4i}+\sqrt{3-4i})^{2}, the initial approach involves expanding the expression, resulting in 6 + 2(\sqrt{3+4i})(\sqrt{3-4i}). The next step is to simplify the term (\sqrt{3+4i})(\sqrt{3-4i}), which can be expressed as \sqrt{(3+4i)(3-4i)}. This product simplifies to \sqrt{3^2 + 4^2} = \sqrt{25} = 5, since it involves multiplying a complex number by its conjugate. The final simplification leads to the expression being equal to 6 + 10, resulting in a total of 16.
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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!
 
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(\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
 

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