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Need solution for RD Sharma maths Class 12 Chapter 5 Determinants Exercise VSQ Question 34 maths textbook solution.

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Answer : a^{2}+b^{2}+c^{2}+d^{2}

Hint: Here we use basic concept of determinant of matrix

Given: \left|\begin{array}{ll} a+i b & c+i d \\ -c+i d & a-i b \end{array}\right|

Solution :

\begin{aligned} &\left|\begin{array}{ll} a+i b & c+i d \\ -c+i d & a-i b \end{array}\right| \\ &=([a+i b][a-i b]-[i d-c][i d+c]) \\ &=\left[a^{2}-(i b)^{2}\right]-\left[(i d)^{2}-c^{2}\right] \\ &=a^{2}-(i b)^{2}-(i d)^{2}+c^{2} \\ &=a^{2}-i^{2} b^{2}-i^{2} d^{2}+c^{2} \end{aligned}

We know that, i^{2}=-1

\begin{aligned} &=a^{2}-(-1) b^{2}-(-1) d^{2}+c^{2} \\ &=a^{2}+b^{2}+c^{2}+d \end{aligned}

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