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The area of the triangle whose vertices ...

The area of the triangle whose vertices are represented by the complex numbers O,z and `z(cos alpha + I sin alpha) (0 lt alpha lt pi)` is equial to -

A

`1/2|z|^(2) cos theta`

B

`1/2 |z|^(2)sin alpha`

C

`1/2 |z|^(2) sin alpha cos alpha `

D

`1/2|z|^(2)`

Text Solution

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The correct Answer is:
B
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AAKASH INSTITUTE-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-Assignment (Section -B) (objective Type Questions ( one option is correct)
  1. If |z1|=2,|z2|=3,|z3|=4 and |2z1+3z2+4z3|=4 then the expression |8z2z3...

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  2. If z1 = cos theta + i sin theta and 1,z1,(z1)^2,(z1)^3,.....,(z1)^(n-1...

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  3. The area of the triangle whose vertices are represented by the complex...

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  4. The maximum value of |z| where z satisfies the condition |z+(2/z)|=2 i...

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  5. The value of (1-tan^2 15^@)/(1+tan^2 15^@) is

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  6. both roots of the equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are

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  7. If log sqrt(3)((|z|^(2)-|z|+1)/(2+|z|))gt2, then the locus of z is

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  8. If arg z = pi/4 ,then

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  9. The z^2 + z|z| + |z|^2 = 0, then locus of Z is

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  10. The least value of p for which the two curves argz=pi/6 and |z-2sqrt(...

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  11. Re((z+4)/(2z-1)) = 1/2, then z is represented by a point lying on

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  12. If f(x) and g(x) are two polynomials such that the polynomial h(x)=xf(...

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  13. The value of (x+omega+omega^(2)) (x +omega^(2)+omega^(4))(x +omega^(...

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  14. If z= (sqrt3-i)/2 , " then " (i^(101)+z^(101))^(103) erqual

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  15. The region of the complex plane for which |(z-a)/(z+veca)|=1,(Re(a) !=...

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  16. If the imaginary part of (2z+1)/(i z+1) is -2 , then show that the loc...

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  17. In z is a complex number stisfying |2008z-1|= 2008|z-2|, then locus z ...

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

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  19. the locus of z=i+2exp(i(theta+pi/4)) is

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  20. If one vertex and centre of a square are z and origin then which of th...

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