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CBSE Class 12 Math 2008 Solved Paper

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Question : 4 of 29
Marks: +1, -0
Evaluate: ∣a+ibc+id−c+ida−ib∣\begin{vmatrix} a+ib & c+id \\ -c+id & a-ib \end{vmatrix}
Solution:  
∣a+ibc+id−c+ida−ib∣\begin{vmatrix} a+ib & c+id \\ -c+id & a-ib \end{vmatrix}
= (a + ib) (a – ib) – (c + id) (-c + id)
= (a2−i2b2)(a^2 - i^2b^2) – (−c2+i2d2)(-c^2 + i^2d^2)
= (a2+b2)(a^2 + b^2) – (−c2−d2)(-c^2 - d^2) (∵ i2i^2 = -1)
= a2+b2+c2+d2a^2 + b^2 + c^2 + d^2
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