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If z=x+i y, z^(1/3)=a-i b " and " x/a-y/...

If `z=x+i y, z^(1/3)=a-i b " and " x/a-y/b=lambda(a^2-b^2),` then `lambda` is equal to

A

3

B

4

C

2

D

none of these

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The correct Answer is:
B
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ML KHANNA-COMPLEX NUMBERS -Problem Set (3) (M.C.Q)
  1. If ( x + iy) ( 2 - 3 i) = 4 + i then

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  2. If ((1 + i) x- 2 i)/( 3 + i) + (( 2 - 3 i ) y + i)/( 3 - i) = i then...

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  3. If z=x+i y, z^(1/3)=a-i b " and " x/a-y/b=lambda(a^2-b^2), then lambda...

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  4. If z = x + iy, , x , y real and | x| + | y| le lambda | z| " then "...

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  5. If sqrt( x + iy) = pm (a + ib) , " then " sqrt( - x - iy) is equal to

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  6. If (x+i y)(p+i q)=(x^2+y^2)i , prove that x=q ,=pdot

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  7. The real part of ( 1- cos theta + 2 i sin theta )^(-1) is

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  8. The number of solutions of the equation z^2=barz is

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  9. The number of solutions of z^(2) + 2 bar(z) = 0 is

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

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  11. The solution of the equation |z|-z=1+2i is

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  12. Find a complex number z satisfying the equation z+sqrt(2)|z+1|+i=0.

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  13. The number of solutions of the system of equations "Re(z^(2))=0, |z|=2...

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  14. The system of equations |z+1-i|=sqrt2 and |z| = 3 has

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  15. The number of jsolutions of the equation z^(2)+barz=0, is

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  16. The number of solutions of the equation z^(3)+barz=0, is

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  17. The number of points in the complex plane that satisfy the conditions ...

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  18. The number of values of z which satisfy both the equations |z-1-i|=sqr...

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  19. The solution of the equation |z|-z=1+2i is

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  20. If z^(2)+(p+iq)z+(r+is)=0, where,p,q,r,s are non-zero has real roots,...

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