Please answer this imaginary question?

Question

Find a solution for the ff: (without the figure i) (in terms of a,b,c and d)
(a + bi)^(c + di)

This might help:
I have discovered that
i^i = e^(-π/2)

E.g.
(2 + 3i)^(1 - 2i)

^_^

Answer 1

This deals with complex numbers and not imaginary
let a= r cos t
b = r sin t

r = sqrt(a^2+b^2)
t= tan ^-1 (b/a)
now (a+ib) = re^(it)
now (a+ib)^(c+id) = (re^(it))^(c+id)
= r^(c+id)*e^(cit-dt)
= r^c e^(cit-dt) r^id

for r = e^(ln r)
r^(id) = (e^(in r)^id)
so result = r^ce^(-dt)e^(cit)e^(idln(r))
= r^ce^(-dt)e^(i(ct-d ln r)
=r^ce^(-dt)(cos(ct-d ln r) + i sin(ct-d ln r))
where r = sqrt(a^2+b^2)
and t = tan^-1(b/a)

Answer 2

the answer is 9.896ac π
~an imaginary answer to an imaginary Question~
lol
^_-

Answer 3

6.5