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Prove that |z-z1|^2+|z-z2|^2 = k will re...

Prove that `|z-z_1|^2+|z-z_2|^2` = k will represent a circle if `|z_1-z_2|^2 le ` 2k.

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A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. If two vertices of an equilateral triangle are z1,z2 then find the com...

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  2. The equation zbarz+abarz+baraz+b=0, b in R represents circle, if

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  3. Prove that |z-z1|^2+|z-z2|^2 = k will represent a circle if |z1-z2|^2 ...

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  4. Find all circles which are orthogonal to |z|=1and|z-1|=4.

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  5. If z=4i-5 then |z| = and barz = .

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  6. If the conjugate of (x +iy) (1-2i) be 1+ i, then:

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  7. If |z|=2 and arg (z)=pi/4 , find zdot

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  8. In the Argand plane, the vector z = 4 - 3i is turned in the clockwise ...

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  9. The value of i^103 + i^(-99) = where i = sqrt(-1) .

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  10. The greatest and the least absolute value of z+1 where |z+4| le3 are ...

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  11. If a+ib = x-iy then in terms of x,y we have a-ib = .

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  12. If n is of the form 3m+2, 1+omega^(-11) +omega^(-2n) = where omega is...

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  13. If alpha,beta,gamma are the cube roots of p then for any x,y and z (xa...

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  14. The value of |sqrtalpha| , where alpha is a nonreal cube root of unity...

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  15. If omega is a cube root of unity, then find the value of the following...

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  16. Let the point P represent the complex number z. If OP is turned round ...

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  17. |sqrtz|^4 = where z is a unimodular complex number.

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  18. (z|barz|^2)/(barz|z|^2) = where z is a complex number of amplitude pi...

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  19. ABCD is a rhombus. Its diagonals AC and BD intersect at the point M a...

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  20. The angle that the vector representing the complex number 1/((sqrt3+i)...

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