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The expression (1+i)^(n1)+(1+i^(3))^(n2)...

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

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Verified by Experts

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

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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))^(n2) is real iff

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  4. If |{:(6i,3i,1),(4,3i,-1),(20,3,i):}|=x+iy, then (x, y) is equal to

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  5. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0,t h e nt ...

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  6. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0,t h e nt ...

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

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

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

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  10. If Re((z+4)/(2z-1)) = 1/2 then z is represented by a point lying on

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  11. The vertices of a square are z(1),z(2),z(3) and z(4) taken in the anti...

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

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  13. If z(1),z(2),z(3), represent vertices of an equilateral triangle such ...

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

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

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

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  17. Show that the complex number z, satisfying the condition arg ((z -1)/(...

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

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

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  20. Let A,B,C be three collinear points which are such that AB.AC=1 and th...

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