Home
Class 12
MATHS
Evaluate (i^(.81) + 1)/(i^(253))^(9)...

Evaluate `(i^(.81) + 1)/(i^(253))^(9)`

Text Solution

Verified by Experts

`( i^(81) + 1)/(i^(253)))^(9) `
`=((i^(2))^(40).i+ 1/((i^(2))^(126).i))^(9)`
`=((-1)^(40)i + 1/((-1)^(126).i))^(9) = (i + 1/i)^(9)`
`(i+1/i^(2))^9 = (i-i)^(9)`
= `(0)^(9) =0`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE|Exercise Try Yourself|60 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE|Exercise Assignment (Section -A) (objective Type Questions ( one option is correct)|47 Videos

  • BINOMIAL THEOREM

    AAKASH INSTITUTE|Exercise Assignment (section-J) Objective type question (Aakash Challengers Questions)|4 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE|Exercise SECTION - J ( Aakash Challengers Questions )|14 Videos

Similar Questions

Explore conceptually related problems

i^(9)+i^(19)

i^(9)+i^(19)

Evaluate: " "(i)" "(i^(41)+(1)/(i^(71)))" "(ii)" "(i^(53)+(1)/(i^(53)))

Evaluate : (i) i^(135) (ii) i^((1)/(47) (iii) (-sqrt(-1))^(4n +3) , n in N (iv) sqrt(-25) + 3sqrt(-4) + 2 sqrt(-9)

Evaluate: int(x^(2)+9)/(x^(4)+81)dx

find the value of (1)/(i)+(1)/(i^(2))+(1)/(i^(3))+(1)/(i^(4))

Evaluate: (i^(2)+i^(4)+i^(6)+i^(7))/(1+i^(2)+i^(3))

Evaluate 1+i+i^2+i^3

Evaluate the following: (i^(41)+i^((1)/(257)))^(9)

Evaluate: " "(i)" "i^(-50)" "(ii)" "i^(-9)" "(iii)" "i^(-131)

AAKASH INSTITUTE-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-section-J (Aakash Challengers Qestions)
  1. Evaluate (i^(.81) + 1)/(i^(253))^(9)

    Text Solution

    |

  2. Let n be even postiive integer such that n/2 is odd and let alpha(0)...

    Text Solution

    |

  3. Let z(1),z(2),z(3) be complex numbers, not all real, such that |z(1)|...

    Text Solution

    |

  4. Let z(1),z(2),z(3) be complex numbers, such that (i) |z(1)|=|z(2)...

    Text Solution

    |

  5. find all complex numbers z such that |z -|z+1|| = |z+|z-1||

    Text Solution

    |

  6. Suppose p is a polynomial with complex coefficients and an even degree...

    Text Solution

    |

  7. The point A(1),A(2)…… A(10) are equally distributed on a circle of rad...

    Text Solution

    |

  8. Let a and b be positive real numbers with a^(3) +b^(3) = a -b and k...

    Text Solution

    |

  9. Let k be a real number such that the inequality sqrt(x-3) +sqrt(6 -x)...

    Text Solution

    |

  10. If alpha and beta are the roots of the equation x^2 + px -1/(2p^2) =...

    Text Solution

    |

  11. If the roots of the quadratic equation x^2 - ax + 2b = 0 are prime num...

    Text Solution

    |

  12. The number of real solutions of the equation root4(97-x) + root4(x) =5...

    Text Solution

    |

  13. If f(x) is a polynomial of degree at least two with integral co-effic...

    Text Solution

    |

  14. p=(x(1)-x(2))^(2) +(x(1)-x(3))^(2) + .......+(x(1)-x(6))^(2) +(x(2)-x(...

    Text Solution

    |

  15. If x,y,z are three real numbers such that x+ y +z =4 and x^(2) + y^(2...

    Text Solution

    |

  16. If unity is double repeated root of px^3+ g(x^2 + x) +r=0, then

    Text Solution

    |

  17. The number of real solutions of the equation 4x^(99) +5x^(98) + 4x^(9...

    Text Solution

    |