is a

Engineering

Mathematics

Introduction to Determinants

Question

$∣ \begin{array}{ccc} 1 + i & 1 - i & 1 \\ 1 - i & i & 1 + i \\ i & 1 + i & 1 - i \end{array} ∣$ is a

real number

irrational number

complex member

Purely imaginary

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1 + i[i(1 – i) – (1 + i)²] – (1 – i)[(1 – i)² – i(1 + i)] + 1[(1 – i)(1 + i) – i²]

= (1 + i)[1 – I² – 2i] – (1 – i)[1 + l² – 2i – i – i²] + [1 – I² – l²]

= (1 + i)[– 2i² – 2i] – (1 – i)(1 – 3i) + [1 – 2i²]

= (1 + i)[+2 – 2i] – (1 – i)(1 – 3i) – 1

2[1 – I²] – (1 – i)(1 – 3i) – 1

4 – (1 – 3i – i + 3i²) – 1

3 – (1 – 4i – 3)

3 – (– 2 – 4i)

= 5 + 4i

so (c) complex number

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