A) \[(a+b)(c-d)\]
B) \[({{a}^{2}}+{{b}^{2}})({{c}^{2}}-{{d}^{2}})\]
C) \[{{a}^{2}}+{{b}^{2}}-{{c}^{2}}-{{d}^{2}}\]
D) \[{{a}^{2}}-{{b}^{2}}+{{c}^{2}}-{{d}^{2}}\]
Correct Answer: C
Solution :
\[\left| \begin{matrix} a+ib & c+id \\ c-id & a-ib \\ \end{matrix} \right|\] \[=(a-ib)(a-ib)-(c+id)(c-id)\] \[={{a}^{2}}-{{i}^{2}}{{b}^{2}}-({{c}^{2}}-{{i}^{2}}{{d}^{2}})\] \[={{a}^{2}}+{{b}^{2}}-{{c}^{2}}-{{d}^{2}}\]
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