How do I normalize a state vector with numbers in it?

[dingo_d]

Homework Statement

I have a state vector:

$$|\psi\rangle=3|+\rangle+4|-\rangle$$

And I should normalize it. + and - are states. And I'm confused. How to normalize this if I have numbers here.

Since we can write the vector state:

$$|\psi\rangle=\sum_k c_k|e_k\rangle$$ where $$|e_k\rangle$$ are basis and $$c_k$$ are complex coefficients in expansion. And then the normalization condition is:

$$\sum_k |c_k|^2=1$$

But I have numbers here? Should I try and multiplying $$|\psi\rangle$$ with $$\langle\psi |$$? And is $$\langle\psi |$$ then:

$$\langle\psi |=3\langle +| +4\langle -|$$ (I dk, but this feels wrong :\)?

 

[issacnewton]

well if you take the magnitude of this state vector

$$\sqrt{\langle\psi |\psi\rangle}=\sqrt{16+9}=5$$

so the length of the vector is 5. so how do you normalize now ? can you do it ?