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COMPLEX NUMBERS AND QUADRATIC EQUATIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSCOMPLEX NUMBERS AND QUADRATIC EQUATIONS2 Marks
Question
Express $(-\sqrt3 + \sqrt{-2})(2\sqrt3 - i)$ in the form of a + ib.
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Answer

Let z= $(-\sqrt3 + \sqrt{-2})(2\sqrt3 - i)$ = $(-\sqrt3 + \sqrt{2i^2})(2\sqrt3 - i)$ = $(-\sqrt3 + \sqrt{2}i)(2\sqrt3 - i)$
z $= -6 + ​\sqrt3 i + 2\sqrt6 i - \sqrt2 i^2$
z $= (-6 + \sqrt2)+\sqrt3(1 + 2\sqrt2)i$

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