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Complex numbers z1 , z2, z3 are the ver...

Complex numbers `z_1 , z_2, z_3` are the vertices A, B, C respectively of an isosceles right angled triangle with right angle at C. Show that `(z_1-z_2)^2 =2 (z_1 - z_3) (z_3-z_2)`.

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A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
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  2. If z1,z2,z3 be the vertices of an equilateral triangle, show that 1/(z...

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  3. Complex numbers z1 , z2, z3 are the vertices A, B, C respectively of ...

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  4. The points representing cube roots of unity

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  5. z, w, w^2 are the vertices of an equilateral triangle in the Argand pl...

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  6. If a ,b ,c and u ,v ,w are the complex numbers representing the vertic...

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  7. If two consecutive vertices of a regular hexagon be z and barz , find ...

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  8. If z1,z2 are two complex numbers representing two consecutive vertices...

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  9. If two vertices of an equilateral triangle are z1,z2 then find the com...

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

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

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

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

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

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

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

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

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

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

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

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