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If the roots of (z-1)^n=i(z+1)^n are plo...

If the roots of `(z-1)^n=i(z+1)^n` are plotted in ten Argand plane, then prove that they are collinear.

A

lie on a parabola

B

are concylic

C

are collinear

D

the vertices of a triangle

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The correct Answer is:
b
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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Exercise
  1. For any complex number z, the minimum value of |z|+|z-1|

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  2. If (3pi)/(2) gt alpha gt 2 pi, find the modulus and argument of (1 -...

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  3. If the roots of (z-1)^n=i(z+1)^n are plotted in ten Argand plane, then...

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  4. Area of the triangle formed by 3 complex numbers, 1+i,i-1,2i, in the A...

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  5. If omega is a complex cube root of unity, then (1-omega+omega^(2))^(6...

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  6. The locus represented by the equation |z-1| = |z-i| is

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  7. If z=i log(23,t h e ncosz= -1 b. -1//2 c. 1 d. 1//2

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  8. If alpha=cos alpha+i sin alpha, b=cos beta+isin beta,c=cos gamma+i sin...

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  9. lf z1,z2,z3 are vertices of an equilateral triangle inscribed in the c...

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  10. The general value of theta which satisfies the equation (costheta+isin...

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  11. If z is a complex numbers such that z ne 0 and "Re"(z)=0, then

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  12. If z + z^(-1)= 1, then find the value of z^(100) + z^(-100).

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  13. Let A,B and C represent the complex number z1, z2, z3 respectively on ...

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  14. Number of solutions of the equation z^(2)+|z|^(2)=0, where z in C, is

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  15. The number of solutions of the equation z^2+z=0 where z is a a complex...

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  16. The centre of a square is at the origin and one of the vertex is 1-i e...

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  17. Let za n domega be two complex numbers such that |z|lt=1,|omega|lt=1a ...

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  18. The system of equation |z+1+i|=sqrt2 and |z|=3}, (where i=sqrt-1) ha...

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  19. The triangle with vertices at the point z1z2,(1-i)z1+i z2 is

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  20. Let alpha and beta be two fixed non-zero complex numbers and 'z' a var...

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