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If \( z \) is a complex number then the equation \( z^{2}+\mathrm{z}|z| \) \( +\left|z^{2}\right|=0 \) is satisfied by \( \left(\omega\right. \) and \( \omega^{2} \) are imaginary cube roots of unity)
(a) \( z=k \omega \) where \( k \in R \)
(b) \( z=k \omega^{2} \) where \( k \) is non negative real
(c) \( z=k \omega \) where \( k \) is positive real
(d) \( z=k \omega^{2} \) where \( k \in R \).
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