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If |z| =3 , the area of the triangle who...

If `|z| =3` , the area of the triangle whose sides are `z , omega z ` and `z + omega z` (where `omega` is a complex cube root of unity) is

A

`(9 sqrt3)/(4)`

B

`(8 sqrt3)/(2)`

C

`(5)/(2)`

D

`(8 sqrt3)/(3)`

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The correct Answer is:
A
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AAKASH SERIES-COMPLEX NUMBERS-EXERCISE -II
  1. If z(1) = 8 + 4i , z(2) = 6 + 4i and z be a complex number such that ...

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  2. The triangle formed by the points 1 , (1 +i)/(sqrt2) and ias vertices ...

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  3. If |z| =3 , the area of the triangle whose sides are z , omega z and ...

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  4. Let z(1) , z(2) be two roots of the equation z^(2) + az + b = 0 , z be...

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  5. In Argand diagram , O , P , Q represent the origin , z and z +iz resp...

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  6. If a is a complex number and b is a real number then the equation bar...

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  7. The complex numbers z(1) , z(2) and z(3) satisfying (z(1) - z(3))/(z(2...

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  8. The cube roots of unity in an Argand plane represent the vertices of a...

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  9. Let z(1) and z(2) be two non-zero complex numbers such that (z(1))/(z(...

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  10. Let the complex number z(1) , z(2) , z(3) be the vertices of an equila...

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  11. Log (log i) =

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  12. The value of i^(i^(-i…..oo)) = x + iy then x^(2) + y^(2) =

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  13. The real and imaginary parts of log (1 + i) =

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  14. (sin (log i^(i)))^3 + (cos (log i^(i)))^3 =

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  15. z = 6. e^(i (pi)/(3)) then |e^(iz)| =

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  16. tan{ilog((a-ib)/(a+ib))}=

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  17. The locus represented by |z-1|=|z+i| is

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  18. Let z = 1 - t + isqrt(t^(2) + t + 2) , where t is a real parameter . T...

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  19. In the Argand Diagram , all the complex numbers z satisfying |z - 4i| ...

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  20. The region of the argand plane defined by |z-i| + |z +i| le 4 is

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