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Let a complex number alpha,alpha!=1, be ...

Let a complex number `alpha,alpha!=1,` be a rootof hte euation `z^(p+q)-z^p-z^q+1=0,w h e r ep ,q` are distinct primes. Show that either `1+alpha+alpha^2++alpha^(p-1)=0or1+alpha+alpha^2++alpha^(q-1)=0` , but not both together.

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The correct Answer is:
`2^(q) = 1 or 2^(p) = 1 ` is 0 . Hence Proved.
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VMC MODULES ENGLISH-COMPLEX NUMBERS -JEE ARCHIVE
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  2. If one of the vertices of the square circumscribing the circle abs(z-1...

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  3. Let a complex number alpha,alpha!=1, be a rootof hte euation z^(p+q)-z...

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  4. If x+i y=sqrt((a+i b)/(c+i d)) prove that (x^2+y^2)^2=(a^2+b^2)/(c^2+d...

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  5. If x=a+b,y=a alpha+b beta and z=abeta+ b alpha , where alpha and beta...

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  6. Express 1//(1-costheta+2isintheta) in the form x=i y .

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  7. If n is n odd integer that is greater than or equal to 3 but not a mul...

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  8. The real values of xa n dy for which the following equation is satisfi...

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  9. Let the complex numbers z(1),z(2) and z(3) be the vertices of an equ...

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  10. A relation R on set of complex numbers defined by Z(1)RZ(2) hArr (Z(1)...

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  11. Prove that the complex numbers z(1),z(2) and the origin form an equ...

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  12. If roots of an equation x^n-1=0a r e1,a1,2, a(n-1), then the value of...

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  13. Show that the area of the triangle on the Argand diagram formed by the...

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  14. Complex numbers z(1),z(2)andz(3) are the vertices A,B,C respectivelt o...

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  15. If i z^3+z^2-z+i=0 , where i=sqrt(-1) , then |z| is equal to 1 (b) 1/2...

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  16. If |z|<=1,|w|<=1, then show that |z- w|^2<=(|z|-|w|)^2+(argz-argw)^2

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  17. Find the non-zero complex number z satisfying z =i z^2dot

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  18. Let z1 \and\ z2 be the roots of the equation z^2+p z+q=0, where the co...

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  19. Let barz+bbarz=c,b!=0 be a line the complex plane, where bar b is the ...

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  20. If z(1) and z(2) are two complex numbers such that |z(1)| lt 1 lt |z...

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