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A function f is defined on the complex number by f (z) = (a + bi)z, where 'a' and 'b' are positive numbers. This function has the property that the image of each point in the complex plane is equidistant from that point and the origin. Given that `|a+bi|=8` and that `b^2=u/v` where u and v are coprimes . Find value of (u+v) .

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MOTION-COMPLEX NUMBER -EXERCISE - 4 (LEVEL -II) PREVIOUS YEAR - JEE ADVANCED
  1. A function f is defined on the complex number by f (z) = (a + bi)z, wh...

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  2. If w=alpha+ibeta, where beta!=0 and z!=1 , satisfies the condition tha...

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  3. A man walks a distance of 3 units from the origin towards the North...

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  4. If |z|=1a n dz!=+-1, then all the values of z/(1-z^2) lie on a line no...

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  5. A particle P starts from the point z(0)=1+2i, where i=sqrt(-1). It mov...

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  6. Let A ,B ,C be three sets of complex number as defined below A={z : I ...

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  7. Let A,B,C be three sets of complex number as defined below A={z:lm ...

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  8. Let A,B,C be three sets of complex number as defined below A={z:lm ...

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  9. Let z=x+i y be a complex number where xa n dy are integers. Then, the ...

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  10. Let z=costheta+isintheta. Then the value of sum(m->1-15)Img(z^(2m-1)) ...

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  11. Q. Let p and q real number such that p!= 0,p^2!=q and p^2!=-q. if alph...

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  12. Let omega be a complex cube root unity with omega!=1. A fair die is th...

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

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

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

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

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

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

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

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

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

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