Home
Class 11
MATHS
Evaluate [i^(18) + (1/i)^(25)]^(3)...

Evaluate `[i^(18) + (1/i)^(25)]^(3)`

Text Solution

Verified by Experts

The correct Answer is:
`2(1+i)`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    KUMAR PRAKASHAN|Exercise TEXTBOOK BASED MCQS|25 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    KUMAR PRAKASHAN|Exercise LATEST EXAM MCQS|1 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    KUMAR PRAKASHAN|Exercise EXERCISE 5.4|6 Videos

  • BINOMIAL THEOREM

    KUMAR PRAKASHAN|Exercise QUESTION OF MODULE|7 Videos

  • CONIC SECTIONS

    KUMAR PRAKASHAN|Exercise QUESTION OF MODULE|9 Videos

Similar Questions

Explore conceptually related problems

If Sigma_( i = 1)^( 2n) sin^(-1) x_(i) = n pi , then find the value of Sigma_( i = 1)^( 2n) x_(i) .

((1-i)^(3))/(1-e^(3))

Evaluate {:[( 102,18,36),( 1,3,4),( 17,3,6)]:}

For a positive integer n , find the value of (1-i)^(n)(1-(1)/(i))^(n)

Find the value of i^(2017)+i^(2018)+i^(2019)+i^(2020) .

Evaluate the following (i) sin^(-1)( sin.( (-3pi)/4))" "(ii) cot^(-1) ( cot(-4))

Express the following in the form of a+bi, (i) (-5i) (1/8 i) , (ii) (-i)(2i)(-1/8i)^(3)

The polar form of ((i)^(25))^(3) is....

Sum of four consecutive powers of i(iota) is zero. i.e., i^(n)+i^(n+1)+i^(n+2)+i^(n+3)=0,forall n in I. If sum_(n=1)^(25)i^(n!)=a+ib, " where " i=sqrt(-1) , then a-b, is

Evaluate : (i) 2 xx 6! - 3 xx 5! (ii) (8!)/(4!) (iii) (20!)/(18!(20 - 18)!)

KUMAR PRAKASHAN-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-MISCELLANEOUS EXERCISE :
  1. Evaluate [i^(18) + (1/i)^(25)]^(3)

    Text Solution

    |

  2. For any two complex numbers z(1) and z(2), prove that Re (z(1)z(2)) = ...

    Text Solution

    |

  3. Reduce (1/(1-4i) -2/(1+i))((3-4i)/(5+i)) to the standard form.

    Text Solution

    |

  4. If x-iy = sqrt((a+ib)/(c-id)), prove that (x^(2) + y^(2))^(2) = (a^(2)...

    Text Solution

    |

  5. Conver the following in the polar form: (i) (1+7i)/(2-i)^(2), (ii) (...

    Text Solution

    |

  6. Conver the following in the polar form: (i) (1+7i)/(2-i)^(2), (ii) (...

    Text Solution

    |

  7. Solve: 3x^(2) - 4x + 20/3=0

    Text Solution

    |

  8. x^(2)-2x + 3/2=0

    Text Solution

    |

  9. 27x^(2) - 10x +1=0

    Text Solution

    |

  10. 21x^(2) - 28x + 10=0

    Text Solution

    |

  11. If z^(1) =2 -I, z(2)=1+i, find |(z(1) + z(2) + 1)/(z(1)-z(2) + 1)|

    Text Solution

    |

  12. If a+ib = (x+i)^(2)/(2x^(2)+1), prove that a^(2) + b^(2) = (x^(2)+1)^(...

    Text Solution

    |

  13. Let z(1) =2-I, z(2) =-2 + i, Find (i) (Re(z(1)z(2))/barz(1)), (ii) I...

    Text Solution

    |

  14. Find the modulus and argument of the complex number (1+2i)/(1-3i)

    Text Solution

    |

  15. Find the real numbers x and y if (x-iy) (3+5i) is the conjugate of -6 ...

    Text Solution

    |

  16. Find the modulus of (1+i)/(1-i) - (1-i)/(1+i)

    Text Solution

    |

  17. If (x+iy)^(3) = u + iy, then show that u/x + v/y = 4(x^(2)-y^(2))

    Text Solution

    |

  18. If alpha and beta are different complex numbers with |beta|=1, then fi...

    Text Solution

    |

  19. Find the numbers of non-zero integral solutions of the equation |1-i|^...

    Text Solution

    |

  20. If (a+ib)(c+id)(e+if)(g+ih) = A + iB, then show that (a^(2) + b^(2))...

    Text Solution

    |