Home
Class 11
MATHS
Show that (-sqrt(-1))^(4n+3) =i, where n...

Show that `(-sqrt(-1))^(4n+3) =i`, where n is a positive integer.

Text Solution

Verified by Experts

The correct Answer is:
`-i`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CBSE COMPLEMENTARY MATERIAL|Exercise Very Short Answer Type Questions(True or False|5 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CBSE COMPLEMENTARY MATERIAL|Exercise Short Answer Type Questions|49 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CBSE COMPLEMENTARY MATERIAL|Exercise Short Answer Type Questions|49 Videos

  • BINOMIAL THEOREM

    CBSE COMPLEMENTARY MATERIAL|Exercise LONG ANSWER TYPE QUESTIONS(Section-D)|16 Videos

  • COORDINATE GEOMETRY

    CBSE COMPLEMENTARY MATERIAL|Exercise section(D) (Long Answer Type Questions ) (6 Marks)|21 Videos

Similar Questions

Explore conceptually related problems

(-i)^(4n+3), where n Is a positive integer.

((1+i)/(1-i))^(4n+1) where n is a positive integer.

Solve (x-1)^(n)=x^(n), where n is a positive integer.

Prove that 2^(n)>1+n sqrt(2^(n-1)),AA n>2 where n is a positive integer.

Prove that (a)(1+i)^(n)+(1-i)^(n)=2^((n+2)/(2))*cos((n pi)/(4)) where n is a positive integer. (b) (1+i sqrt(3))^(n)+(1-i sqrt(3)^(n)=2^(n+1)cos((n pi)/(3)), where n is a positive integer

If (7 + 4 sqrt(3))^(n) + 5 + t , where n and s are positive integers and t is a proper fraction , show that (1 - t) (s + t) = 1

If the middle term in the expreansion of (1+x)^(2n) is ([1.3.5….(2n-1)])/(n!) (k) , where n is a positive integer , then k is .

If A,=[[3,-41,1]], then prove that A^(n),=[[1+2n,-4n][2n], where n is any positive integer.

Find the value of (-1)^(n)+(-1)^(2n)+(-1)^(2n_1)+(-1)^(4n+2) , where n is any positive and integer.