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Let omega be the complex number cos(2pi/...

Let `omega` be the complex number `cos(2pi/3)+isin(2pi/3)` Then the number of distinct complex numbers z satisfying `abs[[z+1,omega,omega^2],[omega,(z+omega^2),1],[omega^2,1 ,z+omega]]=0` is equals to

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PATHFINDER-COMPLEX NUMBER-QUESTION BANK
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  2. If s(n)=i^n+i^(-n) where i=sqrt(-1) and n is an integer then the total...

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  3. Let omega be the complex number cos(2pi/3)+isin(2pi/3) Then the number...

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  4. if z is any complex number satisfying abs(z-3-2i)le2 then the minimum ...

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  5. Ifomega is a nonreal cube root of unity then (a+bomega+cw^2)/(c+aome...

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  6. If(cosalpha+cosbeta+cosgamma)=0, sinalpha+sinbeta+singamma=0 then show...

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  7. If(cosalpha+cosbeta+cosgamma)=0, sinalpha+sinbeta+singamma=0 then show...

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  8. If 1,2,3 and 4 are the roots of the equation x^4+ax^3+bx^2+cx+d=0 then...

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  9. If z1 and z2 are non zero complex numbers such that abs(z1-z2)=absz1+a...

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  10. If 1,alpha,alpha^2.......alpha^(n-1) are the nth roots of unity then p...

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  11. Prove that ifz1,z2 are two complex numbers and cgt0 then abs((z1+z2)...

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  12. Ifz1,z2,z3 are the vertices of an equilateral triangle with z0 as its ...

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  13. If abs(z+(1/z))=a where z is a complex number find the least and the g...

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  14. A(z1),B(z2),C(z3) are the vertices a triangle ABC inscribed in the cir...

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  15. The roots z1,z2,z3 of the equation x^3+3ax^2+3bx+c=0 in which a,b,c ar...

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  16. Ifa,b,c,p,q,r be six complex numbers such that a/p+b/q+c/r=0and p/a+q/...

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  17. The solution of the equation absz-z=1+2i is

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  18. The amplitude of 1+itan 3pi/5 is

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  19. The locus represented by the equation abs(z-1)=abs(z-i) is

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  20. if x=9^(1/3)9^(1/9)9^(1/27)…..infty,y=4^(1/3)4^(1/9)4^(1/27)…..infty a...

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