The value of the determinant | array ccc 6 & 2 i & 3+ 6 2 & 3 + 8 i & 3 2 + 6 i 8 & 2 + 2…
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
The value of the determinant
\[\left|\begin{array}{ccc} \sqrt{6} & 2 \mathrm{i} & 3+\sqrt{6} \\ \sqrt{2} & \sqrt{3}+\sqrt{8} \mathrm{i} & 3 \sqrt{2}+\sqrt{6} \mathrm{i} \\ \sqrt{8} & \sqrt{2}+\sqrt{2} \mathrm{i} & \sqrt{2}+2 \mathrm{i} \end{array}\right|\], where i = \(\sqrt{-1}\), is
\[\left|\begin{array}{ccc} \sqrt{6} & 2 \mathrm{i} & 3+\sqrt{6} \\ \sqrt{2} & \sqrt{3}+\sqrt{8} \mathrm{i} & 3 \sqrt{2}+\sqrt{6} \mathrm{i} \\ \sqrt{8} & \sqrt{2}+\sqrt{2} \mathrm{i} & \sqrt{2}+2 \mathrm{i} \end{array}\right|\], where i = \(\sqrt{-1}\), is
- complex number
- real number
- irrational number
- rational number
Answer
(A) complex number, (B) real number, (D) rational number
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