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Suppose z1 + z2 + z3 + z4=0 and |z1| = |...

Suppose `z_1 + z_2 + z_3 + z_4=0 and |z_1| = |z_2| = |z_3| = |z_4|=1. If z_1, z_2, z_3 ,z_4 `are the vertices of a quadrilateral, then the quadrilateral can be a (a) parallelogram (c) rectangle (b) rhombus (d) square

A

trapezium

B

rectangle

C

square

D

none of these

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A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. If |z1 |=|z2|=|z3| = 1 and z1 +z2+z3 =0 then the area of the triangle ...

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  2. In the Argand plane |(z-i)/(z+i)| = 4 represents a

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  3. Suppose z1 + z2 + z3 + z4=0 and |z1| = |z2| = |z3| = |z4|=1. If z1, z2...

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  4. If arg (z-z1)/(z2-z1) = 0 for three distinct complex numbers z,z1,z2 ...

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  5. The complex numbers z=x+iy which satisfy the equation |(z-5i)/(z+5i)|=...

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  6. The locus of the points z satisfying the condition arg ((z-1)/(z+1))=p...

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  7. If a r g((z-2)/(z+2))=pi/4 then the locus of z is

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  8. zbarz+abarz+baraz+b=0 where binR represents a real circle of nonzero r...

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  9. Find the value of sqrt(20+48i)

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  10. If i^p=i^q where i^2=-1 then p-q is divisible by 4.

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  11. If z=(2+3i)/(3+2i), then |z|=

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  12. Find the solutions to the equation (z+i)^2 = 16.

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  13. If z is a nonreal compex number and |z|=1 then z^2+1/z^2=2 .

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  14. State true or false: If z= (cos2theta+isin2theta)/(costheta+isintheta)...

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  15. If two nonzero complex numbers z1,z2 be such that z1+z2 is real then t...

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  16. For complex numbersz1=x1+iy1" and " z2=x2+iy2 we write z1 cap z2 if x1...

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  17. If z is a nonzero complex number then (bar(z^-1))=(barz)^-1 .

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  18. If the points P and Q represent the complex numbers z and iz then angl...

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  19. If z1ne-z2 and |z1+z2|=|1/z1 + 1/z2| then :

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  20. Find z, if |(z+1)/(z+i)|=1

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