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If |z-2-3i|^(2) + |z- 5 - 7i|^(2)= lamb...

If `|z-2-3i|^(2) + |z- 5 - 7i|^(2)= lambda` respresents the equation of circle with least radius, then find the value of `lambda`.

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To solve the problem, we need to find the value of \( \lambda \) such that the equation \[ |z - (2 + 3i)|^2 + |z - (5 + 7i)|^2 = \lambda \] represents a circle with the least radius. ...
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CENGAGE ENGLISH-COMPLEX NUMBERS-ILLUSTRATION
  1. How many solutions the system of equations ||z + 4 |-|z-3i|| =5 and...

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  2. Prove that |Z-Z1|^2+|Z-Z2|^2=a will represent a real circle [with cent...

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  3. If |z-2-3i|^(2) + |z- 5 - 7i|^(2)= lambda respresents the equation ...

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  4. If (|2z - 3|)/(|z-i|)= k is the equation of circle with complex numbe...

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  5. Find the point of intersection of the curves a r g(z-3i)=(3pi)/4a n d ...

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  6. If complex numbers z(1)z(2) and z(3) are such that |z(1)| = |z(2)| = |...

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  7. If the triangle fromed by complex numbers z(1), z(2) and z(3) is eq...

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  8. Show that the equation of a circle passings through the origin and...

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  9. The triangle formed by A(z(1)), B(z(2)) and C(z(3)) has its circumc...

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  10. Let vertices of an acute-angled triangle are A(z1),B(z2),a n dC(z3)dot...

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  11. If z1, z2, z3 are three complex numbers such that 5z1-13 z2+8z3=0, the...

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  12. If z=z0+A( z -( z )0), w h e r eA is a constant, then prove that loc...

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  13. z1a n dz2 are the roots of 3z^2+3z+b=0. if O(0),(z1),(z2) form an equi...

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  14. Let z(1),z(2) and z(3) be three complex number such that |z(1)-1|= |z...

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  15. Let the complex numbers z(1),z(2) and z(3) be the vertices of an equ...

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  16. In the Argands plane what is the locus of z(!=1) such that a rg{3/2((2...

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  17. If ((3-z1)/(2-z1))((2-z2)/(3-z2))=k(k >0) , then prove that points A(z...

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  18. If z1, z2, z3 are complex numbers such that (2//z1)=(1//z2)+(1//z3), t...

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  19. A(z1),B(z2),C(z3) are the vertices of he triangle A B C (in anticlockw...

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  20. If one of the vertices of the square circumscribing the circle abs(z-1...

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