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Show that the area of the triagle on the...

Show that the area of the triagle on the argand plane formed by the complex numbers Z, iz and `z+iz`is `(1)/(2)|z|^(2)," where "i=sqrt(-1).`

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
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MCGROW HILL PUBLICATION-COMPLEX NUMBERS -SOLVED EXAMPLES LEVEL 1
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  2. If the imaginary part of (2z + 1)/(iz + 1) is -4, then the locus of th...

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  3. Show that the area of the triagle on the argand plane formed by the co...

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  4. If omega is a complex cube root of unity, then a root of the equation ...

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  5. Let z1 and z2 be two non - zero complex numbers such that z1/z2+z2/z...

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  6. If (1+x+x^2)^n=a0+a1x+a2x^2++a(2n)x(2n), find the value of a0+a6++ ,n ...

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  7. Let z = |(1,1-2i,3+5i),(1+2i,-5,10i),(3-5i,-10i,11)|, then

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  8. if (x+i y)^(1/3) = a+ib then (x/a) + (y/b) equals to

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  9. If z epsilon C, the minimum value of |z| + |z-i| is attained at

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  10. For all complex numbers z1, z2 satisfying |z1| =12 and |z2-3-4i|=5, ...

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  11. If z lies on the circle |z-1|=1, then (z-2)/z is

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  12. If 1, omega, ......,omega^(n-1) are the n^(th) roots of unity,then va...

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  13. If omega = "cos"(pi)/(n) + "i sin" (pi)/(n), then value of 1 + omega +...

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  14. If |z|=1a n dz!=+-1, then all the values of z/(1-z^2) lie on a line no...

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  15. The locus of the center of a circle which touches the circles |z-z1|=a...

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  16. If |z^2-1|=|z|^2+1, then z lies on (a) a circle (b) the imaginar...

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  17. If z^2+z+1=0 where z is a complex number, then the value of (z+1/z)^2+...

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  18. If |z""+""4|lt=3 , then the maximum value of |z""+""1| is (1) 4...

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  19. Let z,w be complex numbers such that barz+ibarw=0 and arg zw=pi Then a...

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  20. If z(1) + z(2) + z(3) = 0 and |z(1)| = |z(2)| = |z(3)| = 1, then value...

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