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If w is an imaginary cube root of...

If w is an imaginary cube root of unity then prove that
If w is a complex cube root of unity , find the value of `(1+w)(1+w^2)(1+w^4)(1+w^8).....` to n factors.

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The correct Answer is:
1; if n is even, – `w^2`; if n is odd
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MOTION-COMPLEX NUMBER -EXERCISE - 3 (LEVEL -III) SUBJECTIVE - JEE ADVANCED
  1. The value of the expression , (2-w)(2-w^2)+2.(3-w)(3-w^2)+....... .......

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  2. If w is an imaginary cube root of unity then prove that (1...

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  3. If w is an imaginary cube root of unity then prove that I...

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  4. Interpret the following locii in z in C. 1lt|z-2i|lt3

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  5. Interpret the following locii in z in C. Im (z)ge1

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  6. Interpret the following locii in z in C

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  7. If |z – 2 + i| ge2, then find the greatest and least value of |z|.

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  8. If |z + 3| le 3 then find minimum and maximum values of |z|

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  9. If |z + 3| le 3 then find minimum and maximum values of |z-1|

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  10. If |z + 3| le 3 then find minimum and maximum values of |z+1|

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  11. If O is origin and affixes of P, Q, R are respectively z, iz, z + iz. ...

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  12. If O is origin and affixes of P, Q, R are respectively z, iz, z + iz. ...

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  13. The region represented by RE(z)<=2, Im(z)<=2 and pi/8<=arg(z)<=(3pi)/8...

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  14. Let I Arg((z-8i)/(z+6))=pmpi/2 II: Re ((z-8i)/(z+6))=0 Show that ...

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  15. if a and bbetween 0 and 1 such that the points (a, 1). (1, b) and (0, ...

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  16. Find the non-zero complex numbers z satisfying z =i z^2dot

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  17. If the complex numbers z1, z2,.......zn lie on te unit circle |z| = 1 ...

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  18. Find the Cartesian equations of the locus of z in the complex plane sa...

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  19. Prove that the complex numbers z1 and z2 and the origin form an isosce...

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  20. If the complex number P(w) lies on the standard unit circle in an Arg...

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