Find all values of : $(2)^{i+1}=?$

Question

Find all values of :

$$(2)^{i+1}=?$$

My Try :

$$i+1=\large\sqrt2e^{\frac{i\pi}4}$$

$$(2)^{\large\sqrt2e^{\frac{i\pi}4}}=?$$

now what ?

Answer 1

$$ 2^{i+1} = e^{ (i + 1) \ln 2} = e^{\ln 2} e^{i\ln 2} = 2(\cos (\ln 2) + i\sin (\ln 2)) $$

Answer 2

$$ 2^{i + 1} = e^{\ln 2} e^{i\ln 2} = 2(\cos \ln 2 + i\sin \ln 2)$$

For more example of such computaion see my answer here.Matrix raised to a matrix: $M^N$, is this possible? with $M,N\in M_n(\Bbb K).$