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Question

If ar=(cos2rπ+isin2rπ)19 , then the value of ∣ ∣a1a2a3a4a5a6a7a8a9∣ ∣ is

A
1
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B
1
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C
0
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D
2
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Solution

The correct option is C 0
Let A=∣ ∣a1a2a3a4a5a6a7a8a9∣ ∣
Here, ar=e2rπ^i9
A=∣ ∣ ∣ ∣e2π^i9e4π^i9e6π^i9e8π^i9e10π^i9e12π^i9e14π^i9e16π^i9e18π^i9∣ ∣ ∣ ∣
A=e2π^i9×e8π^i9×e14π^i9∣ ∣ ∣ ∣1e2π^i9e4π^i91e2π^i9e4π^i91e2π^i9e4π^i9∣ ∣ ∣ ∣
A=0 [Since the rows are equal]
Hence, Option C. is correct

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