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If m,n,p,q are consecutive integers t...

If ` m,n,p,q ` are consecutive integers then the value of `i^(m)+i^(n)+i^(p)+i^(q)` is

A

`1`

B

`4`

C

`0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Since, m,n,p,q are consecutive integers. Therefore, `n=m+1,p=m+2,q=m+3`.
`rArr i^(m)+i^(n)+i^(p)+i^(q)=i^(m)+i^(m+1)+i^(m+2)+i^(m+3)`
`i^(m)(1+i+i^(2)+i^(3))`
`i^(m)(1+i-i)=0`
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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Chapter Test
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  7. If alpha+ibeta=tan^(-1) (z), z=x+iy and alpha is constant, the locus o...

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

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

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  13. |{:("6i " "-3i " "1" ),("4 " " 3i" " -1"),("20 " "3 " " i"):}|=x+iy th...

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

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

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

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

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

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

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

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

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