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The expression (1+i)^(n1)+(1+i^(3))^(n(2...

The expression `(1+i)^(n_1)+(1+i^(3))^(n_(2))` is real iff

A

`n_(1)=-n_(2)`

B

`n_(1)=4r+(-1)^(r )n_(2)`

C

`n_(1)=2r+(-1)^( r)n_(2)`

D

none of these

Text Solution

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The correct Answer is:
b
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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Chapter Test
  1. The value of the expression (1+1/omega)(1+1/omega^(2))+(2+1/omega)(2+...

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  2. The condition that x^(n+1)-x^(n)+1 shall be divisible by x^(2)-x+1 is ...

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  3. The expression (1+i)^(n1)+(1+i^(3))^(n(2)) is real iff

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  4. |{:("6i " "-3i " "1" ),("4 " " 3i" " -1"),("20 " "3 " " i"):}|=x+iy th...

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  5. The centre of a square ABCD is at z0dot If A is z1 , then the centroid...

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  6. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0 and alpha...

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  7. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0 and alpha...

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  8. Sum of the series sum(r=0)^n (-1)^r ^nCr[i^(5r)+i^(6r)+i^(7r)+i^(8r)] ...

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  9. If az(1)+bz(2)+cz(3)=0 for complex numbers z(1),z(2),z(3) and real num...

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  10. If 2z1-3z2 + z3=0, then z1, z2 and z3 are represented by

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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. The vertices of a square are z1,z2,z3 and z4 taken in the anticlockwis...

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  13. Let lambda in R . If the origin and the non-real roots of 2z^2+2z+lam...

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  14. if the complex no z1 , z2 and z3 represents the vertices of an equ...

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  15. If P,P^(') represent the complex number z(1) and its additive inverse ...

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  16. Let A(z(1)),B(z(2)),C(z(3)) be the vertices of an equilateral triangle...

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  17. The area of the triangle (in square units) whose vertices are i, omega...

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  18. The complex number z satisfying |z+1|=|z-1| and arg (z-1)/(z+1)=pi/4, ...

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  19. If A,B,C are three points in the Argand plane representing the complex...

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  20. If z(bar(z+alpha))+barz(z+alpha)=0, where alpha is a complex constant,...

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