Find a couple of complex numbers, such that one number is the square of the other and vice versa.
Rem: There will be more than one solution.
In order that each not be larger than the other or smaller than the other, both must have absolute value of 1, that is, be on the unit circle when represented on the Argand plane.
The obvious solution is at 120° and -120°: -0.5 + sqrt(3)/2*i and -0.5 - sqrt(3)/2*i. In terms of revolutions, 1/3 + 1/3 = 2/3 and 2/3 + 2/3 = 1 + 1/3 which is the same as 1/3 in this context.
e^2*pi*i/3 and e^4*pi*i/3.
Any other solution, I don't know.
Posted by Charlie
on 2014-11-19 08:40:36