Let $z_1 , z_2 $ be two complex numbers that satisfy:
$\dfrac{z_2 } {\bar{z_1}}= \frac{3}{8} \big(\cos(75^{\circ})+i\sin(75^{\circ})\big) $ ,
$z_1 z_2 ^2 = \frac{1}{3} \big(\cos(120^{\circ}) + i\sin(120^{\circ}) \big) $ .
How can I determine with of the following can be a possible value for $ \sqrt{z_1} $ ?
(a) $ \frac{2}{\sqrt{3}} \mbox{cis}(135^{\circ}) $
(b) $ \frac{2}{3} \mbox{cis}(155^{\circ})$
(c) $ \frac{2}{\sqrt{3}} \mbox{cis}(195^{\circ}) $
(d) $ \frac{2}{\sqrt{3}} \mbox{cis}(175^{\circ}) $
(e) $ \frac{2}{3} \mbox{cis}(215^{\circ})$
thanks !!!