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Let omega be the complex number " cos...

Let ` omega ` be the complex number ` " cos " ( 2pi)/(3) + isin (2pi)/(3)` . Then the number of distinct complex number x
satisfying `|{:(z + 1, omega, omega^(2)),(omega , z + omega^(2) ,1),(omega^(2) , 1 , z + omega):}|=0` is equal to __________

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MOTION-COMPLEX NUMBER -EXERCISE - 4 (LEVEL -II) PREVIOUS YEAR - JEE ADVANCED
  1. Let omega be a complex cube root unity with omega!=1. A fair die is th...

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  2. Let z(1) and z(2) be two distinct complex numbers and z=(1-t)z(1)+iz(2...

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

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  4. Match the statement in Column I with those in Column II. [Note : He...

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  5. Let a, b and c be three real numbers satisfying [a" "b" "c][[1,9,7],[...

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  6. Let omega be the solution of x^(3)-1=0 with "Im"(omega) gt 0. If a=2 w...

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  7. Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7...

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  8. If z is any complex number satisfying abs(z-3-2i) le 2, where i=sqrt(-...

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  9. Let omega!=1 be cube root of unity and S be the set of all non-singula...

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  10. Let omega= e^((ipi)/3) and a, b, c, x, y, z be non-zero complex numb...

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  11. Let z be a complex number such that the imaginary part of z is nonzero...

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  12. Let complex numbers alpha " and " (1)/(bar alpha) lies on circles (...

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  13. Let w = (sqrt 3 + iota/2) and P = { w^n : n = 1,2,3, ..... }, Further ...

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  14. Let omega be a complex cube root of unity with omegane1 and P = [pij]...

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  15. Let S=S1 nn S2 nn S3, where s1={z in C :|z|<4}, S2={z in C :ln[(z-...

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  16. Let S=S1 nn S2 nn S3, where s1={z in C :|z|<4}, S2={z in C :ln[(z-...

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  17. Let zk=cos((2kpi)/(10))+isin ((2kpi)/10),k=1,2,......9 {:("List I","...

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  18. For any integer k , let alphak=cos(kpi)/7+isin(kpi)/7,w h e r e i=sqrt...

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  19. Let a,b in R and a^(2) + b^(2) ne 0 . Suppose S = { z in C: z = (1...

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  20. Let P=[{:((-z)^r,z^(2r)),(z^(2r),z^r):}] and Ibe the identity matrix o...

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