যদি   $x = \frac{1}{2} \left ( - 1 + \sqrt{- 3} \right ) \quad\text{and}\quad y = \frac{1}{2} \left ( - 1 - \sqrt{- 3} \right )$ হয় তাহলে x ও y এর মধ্যে সম্পর্ক কী?

$\begin{aligned} x & =\frac{1}{2}(-1+\sqrt{-3}) \\ x & =\frac{1}{2}(-1+\sqrt{3} i) \\ x^{2} & =\frac{1}{4}\left\{(-1)^{2}+2 \sqrt{3} i \cdot(-1)+3 i{ }^{2}\right\}\end{aligned}$

$\begin{array}{l}=\frac{1}{4}(1+3 \sqrt{3} i(-1) 3) \\ =\frac{1}{4}(-3-2 \sqrt{3} i) \\ =\frac{1}{4} \cdot 2(-1-\sqrt{3} i) \\ =\frac{1}{2}(-1-\sqrt{3} i) \\ =y \text { (Given). } \\∴ x^{2}=y .\end{array}$