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The roots z1,z2,z3 of the equation x^3+3...

The roots `z_1,z_2,z_3` of the equation `x^3+3ax^2+3bx+c=0` in which a,b,c are complex number correspond to the points A,B,C on the gaussian pllane. Find the centroid of the triangle ABC and show that it will equilateral if `a^2=b`

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PATHFINDER-COMPLEX NUMBER-QUESTION BANK
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  2. A(z1),B(z2),C(z3) are the vertices a triangle ABC inscribed in the cir...

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  3. 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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  4. 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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  5. The solution of the equation absz-z=1+2i is

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

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

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  8. 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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  9. If the fourth roots of unity are z1,z2,z3,z4 then z1^2+z2^2+z3^2+z4^2 ...

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  10. If i=sqrt(-1) then 4+5(-1/2+(isqrt3)/2)^334+3(-1/2+(isqrt3)/2)^365 is ...

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  11. Let z1 and z2 be the nth roots of unity which subtend a right angle at...

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  12. If x^5=(4-3i)^5 thrn the product of all of its roots (wheretheta=-tan^...

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  13. If omega is an imaginary x^n root of unit then underset(r=1)oversetnsu...

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  14. If omega(ne1) be a cube root of unity and (1+omega^2)^n=(1+omega^4)^n ...

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  15. If absz=1 and z ne+-1 then all the values of z/(1-z^2) lie on

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  16. If (1+2i)/(2+i)=r(costheta+isintheta) then

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  17. If z1=a+ib and z2=c+id are two complex numbers lying on the circle x^...

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  18. Number of solution(s) of the equation absz^2+7z=0 is/are

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  19. If z1=9y^2-4-10ix,z2=8y^2-20i where z1=barz2 then z=x+iy is equal to

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  20. Let z1,z2,z3 be three points on absz=1 let theta1,theta2 and theta3 be...

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