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Evaluate : \(\begin{vmatrix} a\,+ & c\,+ \\[0.3em] -c\,+ & a\,- \\[0.3em] \end{vmatrix}\)

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Best answer

(a + ib)(a - ib) - (c + id)(- c + id)

= [a2 - i2b2] - [i2d2 - c2]

= (a2 + b2) - (- d2 - c2) [∵ i2 = -1]

= a2 +b2 + d2 + c2

= a2 + b2 + c2 + d2 

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