Home
Class 12
MATHS
Show that ((sqrt(3))/(2) + (i)/(2))^(5) ...

Show that `((sqrt(3))/(2) + (i)/(2))^(5)` +` ((sqrt(3))/(2) - (i)/(2))^(5) = -sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
`cos.(5pi)/(6)+isin(5pi)/(6)`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    PREMIERS PUBLISHERS|Exercise Solution to Exercise 2.9|25 Videos
  • COMPLEX NUMBERS

    PREMIERS PUBLISHERS|Exercise Problem for practice|45 Videos
  • COMPLEX NUMBERS

    PREMIERS PUBLISHERS|Exercise Solution to Exercise 2.7|12 Videos
  • APPLICATIONS OF VECTOR ALGEBRA

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE (Answer the following questions)|21 Videos
  • DIFFERENTIALS AND PARTIAL DERIVATIVES

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE|40 Videos

Similar Questions

Explore conceptually related problems

If z = ((sqrt(3))/(2) + (i)/(2))^(107) + ((sqrt(3))/(2)-(i)/(2))^(107) , then show that Im (z) = 0

Show that ((i + sqrt(3))/(-i + sqrt(3)))^(2omega) + ((i - sqrt(3))/(i + sqrt(3)))^(2omega) = -1

Show that 3sqrt2 is irrational.

Show that 5-sqrt3 is irrational.

Show that ( 2 + i sqrt(3))^(10) - (2 - i sqrt(3))^(10) is purely imaginary.

The domain of f(x)=sin^(-1)[2x^2-3],w h e r e[dot] denotes the greatest integer function, is (a) (-sqrt(3/2),sqrt(3/2)) (b) (-sqrt(3/2),-1)uu(-sqrt(5/2),sqrt(5/2)) (c) (-sqrt(5/2),sqrt(5/2)) (d) (-sqrt(5/2),-1)uu(1,sqrt(5/2))

Show that cot (7 (1)/(2)) = sqrt(2) + sqrt(3) + sqrt(4) + sqrt(6) .

Show that 4sin27^0=(5+sqrt(5))^(1/2)-(3-sqrt(5))^(1/2)