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For any three complex numbers z(1),z(2),...

For any three complex numbers `z_(1),z_(2),z_(3)`, if `Delta=|{:(1,z_(1),bar(z_(1))),(1,z_(2),bar(z_(2))),(1,z_(3),bar(z_(3))):}|`, then

A

`Re (Delta) = 0`

B

`Im (Delta) = 0`

C

`Re (Delta) ge 0`

D

`Im (Delta) le 0`

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The correct Answer is:
B
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MCGROW HILL PUBLICATION-COMPLEX NUMBERS -EXERCISE
  1. The number of complex numbers satisfying (1 + i)z = i|z|

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  2. Suppose a, b, c in R and C lt 0. Let z = a + (b + ic)^(2015) + (b-ic)^...

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  3. The number of solutions of z^(2) + |z| = 0 is

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  4. The equation |((1+i)z-2)/((1+i)z+4)|=k does not represent a circle whe...

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  5. If |z| ge 5, then least value of |z - (1)/(z)| is

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  6. Principal argument of z = (i-1)/(i(1-"cos"(2pi)/(7))+"sin"(2pi)/(7)) i...

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  7. If (x+iy) = sqrt((a+ib)/(c+id)) then prove that (x^2 + y^2)^2 = (a^2 ...

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  8. For any three complex numbers z(1),z(2),z(3), if Delta=|{:(1,z(1),bar(...

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  9. If x, y, a, b in R, a ne 0 and (a + ib) (x + iy) = (a^(2) + b^(2))i, t...

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  10. If omega (ne 1) is a cube root of unity, then the value of tan[(omega^...

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  11. If z is purely imaginary and Im (z) lt 0, then arg(i bar(z)) + arg(z) ...

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  12. The inequality a + ib gt c + id is true when

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  13. Let z in C be such that Re(z^(2)) = 0, then

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  14. If z(1),z(2) and z(3),z(4) are two pairs of conjugate complex numbers ...

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  15. If z = x + iy and 0 le sin^(-1) ((z-4)/(2i)) le (pi)/(2) then

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  16. If a gt 0 and z|z| + az + 3i = 0, then z is

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  17. If z is a complex numbers such that z ne 0 and "Re"(z)=0, then

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  18. If zk=cos((kpi)/10)+isin((kpi)/10), then z1z2z3z4 is equal to

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  19. If |z(1)| = |z(2)| = 1, z(1)z(2) ne -1 and z = (z(1) + z(2))/(1+z(1)z(...

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  20. If z in C, then Re(bar(z)^(2))= k^(2), k gt 0, represents

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