Question

Find the value of

`{x}^(i)`
for all x belongs to Real Numbers and i = √(-1).

Answer 1

Answer: cis (ln x) ; x > 0

Explanation:

`x^i`

`= e^(ln(x^i))`

`=e^(i \ln(x))`

= cos (ln x) + i sin (ln x)

AKA: cis (ln x)

NOTE: I found this following formula which you may find useful:

`A^i = x + iy`