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Find the complex number z satisfying R e...

Find the complex number `z` satisfying `R e(z^2) =0,|z|=sqrt(3.)`

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`z = x +iy`
or `z^(2) = x^(2) -y + 2ixy `
` rArr Re(z^(2)) = x^(2) -y^(2)`
Also, `|z| = sqrt(x^(2) + y^(2))`
`rArr x^(2) -y^(2) = 0, x^(2) + y^(2) = 3`
`rArr x^(2) = y^(2) = (3)/(2)`
`rArr x =pm sqrt((3)/(2)), y = pm sqrt((3)/(2))`
`rArr z = pm sqrt((3)/(2)) pm sqrt((3)/(2))i`
Thus, there are four complex numbers.
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