Quantum Mechanics

The following steps explain How to handle a complex power

xa+ib=xa.xib=xa.(elog(x))ib∵

=x^a.e^{ib.log(x)}=x^{a}[cos(b.log(x))+isin(b.log(x))]  (by de Moivres theorem)

In the above result put a=0 and b=1 results in

x^i=[cos(log(x))+isin(log(x))]

(1)

(2)


(3)

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