need help???

Question

define the function 2^z and i^z for complex numbers z.

Answer 1

This involves Euler's equations relating e^ix to the sin and cosine functions. You also need to a little trickery such as realizing that 2 = e^ln(2).

So 2^ix= (e^ln(2))^ix
= e^ix * ln(2)
= cos(x * ln(2)) + i * sin(x * ln(2))

Suggest you go to my listed source to see how to handle complex nubers rather than the pure imaginary number I used.

Answer 2

2^ix= (e^ln(2))^ix
= e^{ix ln(2)}
= cos(ln(2) x ) + i sin ( ln(2) y)