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Ifz1,z2,z3 are the vertices of an equila...

If`z_1,z_2,z_3` are the vertices of an equilateral triangle with `z_0` as its circum centre, the changing origin to `z_0` new vertices become `z_1',z_2',z_3'` show that `z_1'^2+z_2'^2+z_3'^2=0`

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PATHFINDER-COMPLEX NUMBER-QUESTION BANK
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  2. Prove that ifz1,z2 are two complex numbers and cgt0 then abs((z1+z2)...

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

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

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

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  6. 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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  7. 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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  8. The solution of the equation absz-z=1+2i is

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

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

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

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

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

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

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

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

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

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

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

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