Question

if \[i ^{i ^{i ^{i ^{......^{\infty}}}}} \] = A+iB find A^2+ B^2

Answer 1

@electrokid @shubhamsrg @phi @RadEn

Answer 2

My Work

Z = i^Z

log Z = Z log(i)

logZ = Z . i pie/2 .............and i am Stuck form here

Answer 3

log(x+iy) = ?

Answer 4

log(x+iy) = log r + i theta

Answer 5

r = |Z|

Answer 6

substitute z=x+iy and see if it helps
r = sqrt(x^2 + y^2)
theta = tan-1 (y/x)

finally, compare real and imaginary parts

Answer 7

Yup..Got it...THXXX