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A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
- Prove that sqrt(-1-sqrt(-1-sqrt1-… prop=w or w^2 .
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- Resolve into the linear factor: a^3+b^3
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- Resolve into the linear factor: a^3+b^3+c^3-3abc
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- value of the series a(0)-a(2) + a(4)-a(6) +….. is
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- If (1+x)^n=a0+a1x+a2x^2+...+anx^n then find : a1-a3+a5-a7+… .
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- If (1+x)^n=a0+a1x+a2x^2+...+anx^n then find : a0+a3+a6+a9+… .
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- If (1+x+x^2)^n=a0+a1x+a2x^2++a(2n)x(2n), find the value of a0+a6++ ,n ...
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- If 1,a1,a2,a3,…,a(n-1) are the nth roots of unity then prove that : (1...
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- If 1,a1,a2,a3,…,a(n-1) are the nth roots of unity then prove that : 1+...
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- If alpha is an n^(th) roots of unity, then 1+2alpha+3alpha^(2)+……..+n...
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- If alpha (!=1) is a nth root of unity then S = 1 + 3alpha+ 5alpha^2 + ...
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- sum(p=1)^pi(3p+2)[sum(q=1)^10sin(2qpi)/11-icos(2qpi)/11]^p
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- Show that the polynomial x^(4p)+x^(4q+1)+x^(4r+2)+x^(4s+3) is divisibl...
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- If alpha ia ROOT OF x^2+x+1= 0 then show that alpha is also a root of...
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- If p,q,r are three consecutive integers ge3, prove that x^p+x^q+x^r is...
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- If n is n odd integer that is greater than or equal to 3 but not la ul...
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- If z^2(bar omega)^4=1 where omega is a nonreal complex cube root of 1 ...
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- Find z satisfying |z-5i|le3 such that amp z is the minimum.
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- If |z-25i| lt= 15. then |"maximum " arg(z) - "minimum " arg(z)| equals
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- Find the complex number Z, the greatest in absolute value which satisf...
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