is

Engineering

Mathematics

Introduction to Determinants

Question

$[\begin{matrix} cosα + isinα & cosβ + isinβ \\ sinβ + icosβ & sinα + icosα \end{matrix}]$ is

2 cosα

2 sinβ

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Let $[\begin{matrix} cosα + isinα & cosβ + isinβ \\ sinβ + icosβ & sinα + icosα \end{matrix}]$
|A| = (cosα + isinα) (sinα + icosα) – (cosβ + isinβ) (sinβ + icosβ)
= cosαsinα + i – cosαsinα – [cosβsinβ + isinβcosβ]

= 0

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