First slide

Algebra of complex numbers

Question

If $ω \neq 1$ is a cube root of unity, then $|\begin{array}{ccc} 1 & 1 + i + ω^{2} & ω^{2} \\ 1 - i & - 1 & ω^{2} - 1 \\ - i & - i + ω - 1 & - 1 \end{array}|$ equal

Moderate

A

0
B

1
C

$i$
D

$ω$

Solution

Use $R_{2} \to R_{2} - R_{1} - R_{3}$ , then the first row of the determinant elements are all zero's, hence the determinant value=0

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