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Find the value of i^n+i^(n+1)+i^(n+2)+i^...

Find the value of `i^n+i^(n+1)+i^(n+2)+i^(n+3)` for all `n in Ndot`

A

`0`

B

`i`

C

`-i`

D

`2i ^(n)`

Text Solution

Verified by Experts

The correct Answer is:
A
`i^(n) + i^(n+1) + i^(n+2) + i^(n+3) = i^(n)[1+ i^(2)+ i^(3)]`
`=i ^(n) [ 1+ i- 1-i]`
` = i^(n) (0) = 0`
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CENGAGE ENGLISH-COMPLEX NUMBERS-ILLUSTRATION
  1. Evaluate : (i) i^(135) (ii) i^(-47) (iii) (-sqrt(-1))^(4n +3)...

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  2. Find the value of i^n+i^(n+1)+i^(n+2)+i^(n+3) for all n in Ndot

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  3. Find the value of 1+i^2+i^4+i^6++i^(2n)

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  4. Show that the polynomial x^(4p)+x^(4q+1)+x^(4r+2)+x^(4s+3) is divisibl...

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  5. Solve: i x^2-3x-2i=0,

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  6. If z=4+isqrt(7) , then find the value of z^2-4z^2-9z+91.

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  7. Express each of the following in the standerd from a + ib (i) (5+...

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  8. The root of the equation 2(1 + i) x^2-4(2-i) x-5-3 i = 0, where i = sq...

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  9. Find the value of (1+ i)^(6) + (1-i)^(6)

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  10. If ((1+i)/(1-i))^m=1, then find the least positive integral value of m...

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  11. Prove that the triangle formed by the points 1,(1+i)/(sqrt(2)),a n di ...

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  12. Find real q such that (3+2isintheta)/(1-2isintheta) is purely real.

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  13. If the imaginary part of (2z+1)//(i z+1) is -2, then find the locus of...

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  14. If z is a complex number such that |z - barz| +|z + barz| = 4 then fi...

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  15. If (x+i y)^5=p+i q , then prove that (y+i x)^5=q+i pdot

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  16. If z = x + iy lies in the third quadrant, then prove that (barz)/(z) ...

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  17. Let z = ((sqrt(3))/(2) + (i)/(2))^(5)+((sqrt(3))/(2)-(i)/(2))^(5). If ...

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  18. Find the relation if z1, z2, z3, z4 are the affixes of the vertices of...

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  19. Let z1, z2, z3 be three complex numbers and a ,b ,c be real numbers no...

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  20. Find real values of x and y for which the complex numbers -3+i x^2y an...

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