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If `z_1=a_ib and z_2=c+id` are complex numbes such that `|z_1|=|z_2|=1 and Re(z_1barz_2)=0` then the pair of complex numbers `omega_1= a+ic and omega_2=b+id` satisfy which of the following relations? (A) `|omega_1|=1` (B) `|omega_2|=1` (C) `Re(omega_1 baromega_2)=0` (D) `Im(omega_1baromega_2)=0`

A

`|w_1|`=1

B

`|w_2|`=1

C

Re(`w_1barw_2`)=0

D

none of these

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A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
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  2. Let z1 and z2 be complex numbers of such that z1!=z2 and |z1|=|z2|. I...

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  3. If z1=aib and z2=c+id are complex numbes such that |z1|=|z2|=1 and Re(...

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  4. if |z1|= |z2| ne 0 and amp (z1)/(z2)=pi then

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  5. If z1 and z2 are two nonzero complex numbers such that |z1-z2|=|z1|-|z...

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  6. If z1,z2 are nonreal complex and |(z1+z2)/(z1-z2)|=1 then (z1)/(z2) is

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  7. If z=2+3i, then |z^2|^3 is equal to

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  8. The equation z^5+z^4+z^3+z^2+z+1=0 is satisfied by

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  9. The points, z1,z2,z3,z4, in the complex plane are the vartices of a pa...

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  10. If z^4= (z-1)^4 then the roots are represented in the Argand plane by...

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  11. If |z1 |=|z2|=|z3| = 1 and z1 +z2+z3 =0 then the area of the triangle ...

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  12. In the Argand plane |(z-i)/(z+i)| = 4 represents a

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  13. Suppose z1 + z2 + z3 + z4=0 and |z1| = |z2| = |z3| = |z4|=1. If z1, z2...

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  14. If arg (z-z1)/(z2-z1) = 0 for three distinct complex numbers z,z1,z2 ...

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  15. The complex numbers z=x+iy which satisfy the equation |(z-5i)/(z+5i)|=...

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

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  17. If a r g((z-2)/(z+2))=pi/4 then the locus of z is

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  18. zbarz+abarz+baraz+b=0 where binR represents a real circle of nonzero r...

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  19. Find the value of sqrt(20+48i)

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  20. If i^p=i^q where i^2=-1 then p-q is divisible by 4.

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