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Principal argument of $z = \frac{i - 1}{i (1 \cos \frac{2 π}{7}) + \sin \frac{2 π}{7}}$ is

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a

π28

b

3π28

c

17π28

d

19π28

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detailed solution

Correct option is C

i1−cos⁡2π7+sin⁡2π7=2isin2⁡π7+2sin⁡π7cos⁡π7=2sin⁡π7cos⁡π7+isin⁡π7Also , i−1=2−12+i2=2cos⁡3π4+isin⁡3π4∴ z=22sin⁡π7cos⁡3π4−π7+isin⁡3π4−π7 =22sin⁡π7cos⁡17π28+isin⁡17π28Thus , arg⁡(z)=17π28.

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