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Find the number of solutions of z^2+|z|^...

Find the number of solutions of `z^2+|z|^2=0.`

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Let, `z=x+iy`, then
`z^2+|z|^2=0=>(x+iy)^2+|x+iy|^2=0`
`=>x^2-y^2+2xyi+x^2+y^2=0`
`=>2x^2+2xyi=0`
...
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