Show the following quadratic equation: x^2-(32-2i)x-2 i=0 - Vidyadip

Question

Show the following quadratic equation:
$\text{x}^2-(3\sqrt{2}-2\text{i})\text{x}-\sqrt{2}\text{ i}=0$

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Answer

We will apply discriminate rule on ax² + bx + c = 0
$\text{x}=\frac{-\text{b}\pm\sqrt{\text{b}^2-4\text{ac}}}{2\text{a}}$
Now,
$\text{x}^2-(3\sqrt{2}-2\text{i})\text{x}-\sqrt{2}\text{ i}=0$
$\text{x}=\frac{(3\sqrt{2}-2\text{i})\pm\sqrt{[-(3\sqrt{2}-2\text{i})]^2-4(1)(-\sqrt{2})\text{i}}}{2(1)}$
$=\frac{(3\sqrt{2}-2\text{i})\pm\sqrt{(3\sqrt{2})-2\text{i})^2+4\sqrt{2}\text{i}}}{2}$
$=\frac{3\sqrt{2}-2\text{i}}{2}\pm\frac{4-\sqrt{2}\text{i}}{2}$

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