Home
Class 12
MATHS
If z=e^((2pi i)/5), then 1+z+z^(2)+z^(3)...

If `z=e^((2pi i)/5)`, then `1+z+z^(2)+z^(3)+5z^(4)+4z^(5)+4z^(6)+4z^(7)+4z^(8)+5z^(9)=`

A

`0`

B

`4z^(3)`

C

`5z^(4)`

D

`-4z^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `(1+z+z^(2)+z^(3)+z^(4))+4z^(4)(1+z+z^(2)+z^(3)+z^(4))+5z^(9)`.
`=(1-z^(5))/(1-z)+4z^(4)((1-z^(5))/(1-z))+5z^(4)`
`=5z^(4)` `(:'z^(5)=1)`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|11 Videos

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise Matching Column|1 Videos

  • CIRCLES

    CENGAGE PUBLICATION|Exercise Comprehension Type|8 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos

Similar Questions

Explore conceptually related problems

z=i^5 then the value of (z+z^2+z^3+z^4)

If z=4+3i, then find z-barz

If z=4-3i, then find z-barz

Let fourth roots of unity be z_(1),z_(2),z_(3) and z_(4) respectively. Statement - I: z_(1)^(2)+z_(2)^(2)+z_(3)^(2)+z_(4)^(2)=0 Statement - II: z_(1)+z_(2)+z_(3)+z_(4)=0

Solve for z : z^2-(3-2i)z=(5i-5)dot

If |(Z-5i)/(Z+5i)|=1 ,then show that Z in R

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

If 8iz^3+12z^2-18z+27i=0, then (a). |z|=3/2 (b). |z|=2/3 (c). |z|=1 (d). |z|=3/4

Find the value of each of the following polynomials for the indicated value of variables: (i) p(x) = 4x ^(2) - 3x + 7 at x =1 (ii) q (y) = 2y ^(3) - 4y + sqrt11 at y =1 (iii) r (t) = 4t ^(4) + 3t ^(3) -t ^(2) + 6 at t =p, t in R (iv) s (z) = z ^(3) -1 at z =1 (v) p (x) = 3x ^(2) + 5x -7 at x =1 (vi) q (z) = 5z ^(3) - 4z + sqrt2 at z =2

If A(z_(1)) , B(z_(2)) , C(z_(3)) are vertices of a triangle such that z_(3)=(z_(2)-iz_(1))/(1-i) and |z_(1)|=3 , |z_(2)|=4 and |z_(2)+iz_(1)|=|z_(1)|+|z_(2)| , then area of triangle ABC is