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NIMCET Previous Year Questions (PYQs)

NIMCET Complex Number PYQ



If xk=cos(2πkn)+isin(2πkn) , then nk=1(xk)=?





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Solution

Sum of Complex Roots of Unity

Given:

xk=cos(2πkn)+isin(2πkn)=e2πik/n

Required: Find: nk=1xk

This is the sum of all nth roots of unity (from k=1 to n).

We know: n1k=0e2πik/n=0 So shifting index from k=1 to n just cycles the same roots: nk=1e2πik/n=0

✅ Final Answer:   0



If |z|<31, then |z2+2zcosα| is





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Solution



A particle P starts from the point






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Solution




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