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Question

Find all complex numbers z which satisfy the following equation
z2+|z|=0.

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Solution

x2y2+i2xy+x2+y2=0
x2y2+x2+y2=0
2xy=0 x=0 or y=0
When x=0 then y2±y=0 .. y=0,±1
(0,0),(0,1),(0,1) or z=0,i,i
When y=0 then we will get (0,0), (1,0) and (1,0).
But these not complex numbers.
Hence 0,i,i are the only three solutions of the given equation.

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