Number of elements in a multiplicative group of $ (complex)^{2^n} $ th roots of unity for a specific n.

Question

The number of elements of the multiplicative group $ (complex)^n $ th roots of unity is n .But for a fixed n the number of elements in a multiplicative group of $ (complex)^{2^n}$ th roots of unity is also n .I didn't know that I thought it's $ 2^n $ but few days ago I saw someone wrote $ G_{2^n} =\{e^{\frac{2\pi ik}{2^n}} \mid k=0,1,2,...n-1\} $ which means there are n elements .So Is there a definition I mean what about the number of elements of the multiplicative group $ (complex)^{4^3} $ th roots of unity is it 64 or 6 or 3. Thanks in advance.