solve z^2 = iZ (1 Viewer)

[Mumma]

Z is conjugate z

z² = iZ

 

[shimmerz_777]

i just tried it then, for some reason i got real and imaginary parts equaling 0, ill try again, mayb thats not the only answer

 

[shimmerz_777]

on second thought i found a mistake,

let z = x + iy
(x + iy)^2 = i (x-iy)
x^2 - y^2 +2ixy = y + ix
equating real and imaginary

2xy = x.... 2y=1 y= 1/2

x^2 - y^2 = y
x^2 - 1/4 = 1/2

x= sqrt 3/4

 

[shimmerz_777]

ha ive done it again with u

 

[suamara]

2xy=x

x(2y-1) =0

x=0 , y=1/2


ie x=0 is a solution as well

 

[shimmerz_777]

where does the z=i come from?

EDIT-- oh i see dont worry

 

[STx]

so how did u find the z=i solution?, i know it satisfies the equation though..

 

[shimmerz_777]

check suamara's line