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For every real number c ge 0, find all c...

For every real number c `ge` 0, find all complex numbers z which satisfy the equation `abs(z)^(2)-2iz+2c(1+i)=0`, where `i=sqrt(-1)` and passing through (-1,4).

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A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. IF 1age1, find all complex numbers z satisfying the equatioin z+a|z+|+...

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  2. Find all complex numbers satisfying barz= z^2 .

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  3. For every real number c ge 0, find all complex numbers z which satisfy...

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  4. Let the complex numbers z of the form x+iy satisfy arg ((3z-6-3i)/(2z-...

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  5. If z = x + iy and |z+6| = |2z+3| , prove that x^2+y^2=9.

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  6. if argument of (z-1)/(z+1)=pi/4 then prove that x^2+y^2-2y=1

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  7. If z is a normal complex for which |z| = 1 , prove thatfrac (z-1)(z+1...

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  8. Show that a real value of x will satisfy hte equation (1-i x)//(1+i x)...

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  9. If (a1+ib1)(a2+ib2)...(an+ibn) = x+iy , prove that : (a1^2+b1^2)(a2^2+...

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  10. If (a1+ib1)(a2+ib2)...(an+ibn) = x+iy , prove that : tan^-1frac(b1)(a1...

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

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  12. Show that if iz^3+z^2-z+i=0, then |z|=1

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  13. If f(z) = a0z^n+a1z^(n-1)+a2z^(n-2)+...+an where z is a complex numbe...

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  14. If |z1+z2| = |z1-z2|, prove that ampz1 - ampz2 = pi/2 .

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  15. Prove that |z1+z2|^2 = |z1|^2+|z2|^2 if z1/z2 is purely imaginary.

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  16. Prove that |z1+z2|^2+|z1-z2|^2 =2|z1|^2+2|z2|^2.

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  17. Prove that |alpha+sqrt(alpha^2-beta^2)|+|alpha-sqrt(alpha^2-beta^2)|= ...

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  18. Prove that |1-barz1z2|^2-|z1-z2|^2=(1-|z1|^2)(1-|z2|^2).

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  19. If |z-1| <3, prove that |iz+3-5i| < 8.

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  20. Prove that for nonzero complex numbers |z1+z2| |frac(z1)(|z1|)+frac(z2...

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