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The area of the triangle on the complex ...

The area of the triangle on the complex plane formed by the complex number `z,-i z` and `z+i z` is

A

`|z|^(2)`

B

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

C

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

D

`(sqrt(3))/(4)|z|^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
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HIMALAYA PUBLICATION-COMPLEX NUMBERS-QUESTION BANK
  1. If alpha and beta are the root of the equation x^(2)-x+1=0 then alpha...

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  2. The number of complex numbers z such that |z-1|=|z+1|=|z-i| equals

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  3. If (omega ne 1) is a cube root of unity and (1+omega)^(7)=A+Bomega. Th...

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  4. If |z|=1 and z ne pm 1, then all the values of (z)/(1-z^(2)) lie on

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  5. Points z in the complex plane satisfying Re(z+1)^(2)=|z|^(2)+1 lies on

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  6. Let omega be the complex number cos (2 pi)/(3)+i sin (2 pi)/(3) . Then...

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  7. If |w|=1, then the set of points z=w+(1)/(w) is contained in or equal ...

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  8. i^(2)+i^(4)+i^(6)+ldots . .(2 n+1) terms =

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  9. The value of sum(k=1)^(6)("sin"(2pik)/(7)-I"cos"(2pik)/(7)) is

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  10. If the imaginary part of (2z+1)/(iz+1) is -2, then the locus of the po...

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  11. If |z|ltsqrt(2)-1, then |z^(2)+2 z cos alpha| is less than

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  12. The area of the triangle on the complex plane formed by the complex nu...

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  13. If z=x+i y, z^(1 / 3)=a-i b and (x)/(a)-(y)/(b)=k(a^(2)-b^(2)) then th...

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  14. The complex plane of z=x+iy, which satisfies the equation |(z-5i)/(z+5...

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  15. If Im((z-1)/(2 z+1))=-4 then the locus of z is

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  16. If 1,a(1), a(2). ..., a(n-1) are n roots of unity, then the value of (...

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  17. If |(z+i)/(z-i)|=sqrt(3), then the radius of the circle is

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  18. If sqrt(3)+i=(a+i b)(c+i d) then tan ^(-1) (b/a)+tan ^(-1) (d/c)=

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  19. Find the numbers of non-zero integral solutions of the equation |1-i|^...

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  20. The region of the complex plane for which |(z-a)/(z+a)|=1,(Re) ne 0, i...

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