Evaluate the determinants:

$$\begin{bmatrix}a+ib &c+id \\[0.3em] -c+id & a-ib \\[0.3em] \end{bmatrix}$$

Asked by Aaryan | 1 year ago |  184

Solution :-

|A| = (a + ib) (a – ib) – (c + id) (–c + id)

= (a + ib) (a – ib) + (c + id) (c – id)

= a2 – i2 b2 + c2 – i2 d2

We know that i2 = -1

= a2 – (–1) b2 + c2 – (–1) d2

= a2 + b2 + c2 + d2

Answered by Sakshi | 1 year ago

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