How Do I Prove This Vector Space Equality?

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To prove the vector space equality, begin by recognizing that V is a vector space over the complex numbers, not contained in C. The key is to utilize the property that the norm squared of a vector is given by ||v||² = <v, v>. Expanding the expressions ||u + v||, ||u - v||, ||u + iv||, and ||u - iv|| will lead to the necessary components for the proof. This approach will help clarify the relationships between the vectors involved. Following these steps should provide a clearer path to demonstrating the equality.
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Homework Statement



Hey guys.
Can anyone help with proving this equality please?
I don't have a clue.

10x.

Homework Equations





The Attempt at a Solution

 

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First V is not contained in C, V is a vector space over the complex numbers.

Now, presumably you know that ||v||2= <v, v>.

Expand ||u+ v||, ||u- v||, ||u+ iv||, and ||u- iv|| and see what you get.
 
HallsofIvy said:
First V is not contained in C, V is a vector space over the complex numbers.

Now, presumably you know that ||v||2= <v, v>.

Expand ||u+ v||, ||u- v||, ||u+ iv||, and ||u- iv|| and see what you get.

Thanks.
 

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