If Z = \frac{1}{3}\begin{vmatrix}i & 2i & 1 \\ 2i & 3i & 2 \\ 3 & 1 & 3\end{vmatrix} = x + iy; i=\sqrt{-1} then what is modulus of Z equal to?

Explanation

Expanding the determinant along the first row: D = i(9i - 2) - 2i(6i - 6) + 1(2i - 9i) = -9 - 2i + 12 + 12i - 7i = 3 + 3i. Thus Z = \frac{1}{3}(3+3i) = 1+i. The modulus is |Z| = \sqrt{1^2 + 1^2} = \sqrt{2}.

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