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if iz^3+z^2-z+i=0 then show that absz=1...

if `iz^3+z^2-z+i=0` then show that `absz=1`

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PATHFINDER-COMPLEX NUMBER-QUESTION BANK
  1. If in argand plane the vertices A,B,C of an isoceles triangle are rep...

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  2. let z1=10+6i and z2=4+6i if z is nay complex number such that argument...

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  3. if iz^3+z^2-z+i=0 then show that absz=1

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  4. let z1 and z2 be roots of the equation z^2+pz+q=0 where the coefficien...

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  5. For complex numbers z and w prove that absz^2w-abs(w)^2z=z-w if and on...

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  6. if z1 and z2 are two complex numbers such that absz1lt1ltabsz2 then p...

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  7. find the centre and radius of the circle formed by all the points repr...

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  8. Let omega ne1 be a complex cube root of unity if (3-3omega+2omega^2)^(...

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  9. For any integer k let alphak=cos((kpi)/7)+isin((kpi)/7) where i=sqrt(-...

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  10. A complex number z is said to be unimodular if absz=1 suppose z1 and z...

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  11. The value of ((1+sqrt3i)/(1-sqrt3i))^64+((1-sqrt3i)/(1+sqrt3i))^64

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  12. Find the maximum value of absz when abs(z-3/z)=2 ,z being a complex nu...

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  13. If z is a complex number such that abszge2 then the minimum value of a...

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  14. Let z1,z2 be two fixed complex numbers in the Argand plane and z be an...

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  15. In the Argand plane the distinct roots of 1+z+z^3+z^4=0 (z is a comple...

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  16. Suppose that z1, z2, z3 are three vertices of an equilateral triangle ...

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  17. The value of absz^2+abs(z-3)^2+abs(z-i)^2 is minimum when z equals

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  18. Let z1 be a fixed point on the circle of radius 1 centered at the orig...

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  19. Let alpha ,beta denote the cube roots of unity other than 1 and alpha ...

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  20. Let complex numbers alpha and 1/alpha^- lie on circles (x-x0)^2+(y-y0...

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