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A symmetric relation (Posted on 2014-11-19) Difficulty: 3 of 5
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.

See The Solution Submitted by Ady TZIDON    
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solution | Comment 1 of 5
x=y^2 (1)
y=x^2 (2)

(1)-(2) gives

first we have y-x=0 as a solution
giving y=x thus
x=x^2 thus
x=0 or x=1 giving the solutions (0,0) and (1,1)

if y-x is not zero then we have
y=-x-1 giving
x=-1/2+i*sqrt(3)/2 or x=-1/2-i*sqrt(3)/2
y=-1/2-i*sqrt(3)/2 and y=-1/2+i*sqrt(3)/2 respectively
thus we have three distinct solutions

  Posted by Daniel on 2014-11-19 08:28:56
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