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For all real numbers x, let the mapping ...

For all real numbers x, let the mapping `f (x) = 1/(x-i)`. where `i =sqrt -1`. If there exist real number `a, b, c and d` for which `f(a), f(b), f(c) and f(d)` form a square on the complex plane. Find the area of the square.

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MOTION-COMPLEX NUMBER -EXERCISE - 3 (LEVEL -III) SUBJECTIVE - JEE ADVANCED
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  2. If O is origin and affixes of P, Q, R are respectively z, iz, z + iz. ...

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

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

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

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

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

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

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

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

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  11. Let z=x+i y be a complex number, where xa n dy are real numbers. Let A...

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  12. For all real numbers x, let the mapping f (x) = 1/(x-i). where i =sqrt...

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  13. Given that |z-1|=1, where z is a point on the argand planne , show...

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  14. Dividing f(z) by z- i, we obtain the remainder i and dividing it by z...

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  15. If the equation x^4+ax^3+bx^2+cx+d=0 has four imaginary roots two with...

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  16. If z1, z2 are the roots of the equation az^2 + bz + c = 0, with a, b, ...

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  17. Find the set of points on the argand plane for which the real part of ...

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  18. The equation z^n – 1 = 0 has n roots which are called the nth roots o...

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  19. The equation z^n – 1 = 0 has n roots which are called the nth roots o...

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  20. MATCH THE COLUMN {:(Column-I,Column-II),("(A) If "|ai|lt1,lamda1ge0 ...

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