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If `a ,b ,c` and `u ,v ,w` are the complex numbers representing the vertices of two triangles such that `(c=(1-r)a+r b` and `w=(1-r)u+r v ,` where `r` is a complex number, then the two triangles have the same area (b) are similar are congruent (d) None of these

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A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. The points representing cube roots of unity

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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