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

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

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise QUESTIONS FROM NCERT EXEMPLAR|10 Videos

  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise EXERCISE|10 Videos

  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise NCERT EXERCISE 5.3|10 Videos

  • BINOMIAL THEOREM

    MODERN PUBLICATION|Exercise COMPETITION FILE (JEE MAIN)|11 Videos

  • CONIC SECTIONS

    MODERN PUBLICATION|Exercise CHAPTER TEST 11|12 Videos

Similar Questions

Explore conceptually related problems

Evaluate: [i^(19)+((1)/(i))^(25)]^(2)

Find the values of [i^18+(1/i)^25]^3

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

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

Express the following in the standard form a + ib: (i^(18)+((1)/(i))^(25))^(3)

Evaluate (i^17-1/i^34)^3 .

Simplify the following : (i) [i^(19) +(1)/(i^(25))]^(2) (ii) [i^(5)- (1)/(i^(3))]^(4)

Show that: {i^(19)+((1)/(i))^(25)}^(2)=-4( ii) {i^(17)-((1)/(i))^(34)}^(2)=2i (iii) {i^(18)+((1)/(i))^(24)}^(3)=0 (iv) i^(n)+i^(n+1)+i^(n+2)+i^(n+3)=0 for all n in N.

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

Find the value of (1+i)^(3)+(1-i)^(6)

MODERN PUBLICATION-COMPLEX NUMBERS-MISCELLANEOUS EXERCISE ON CHAPTER
  1. Evaluate : [i^(18)+(1/i)^(25)]^3

    Text Solution

    |

  2. Prove that Re (z1 z2)= Re z1 Re z2 - Imz1 Imz2 ,

    Text Solution

    |

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

    Text Solution

    |

  4. If x - i y =sqrt((a-i b)/(c-i d))prove that x^2+y^2=(a^2+b^2)/(c^2+d^2...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. Solve the equation :x^2-2x+3/2=0

    Text Solution

    |

  8. Solve the equation :27 x^2-10 x+1=0

    Text Solution

    |

  9. Solve the equation :21 x^2-28 x+10=0

    Text Solution

    |

  10. If z1=2-i ,\ z2=1+i , find |(z1+z2+1)/(z1-z2+i)|

    Text Solution

    |

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

    Text Solution

    |

  12. Let z1=2-i ,z2=-2+i. Find (i) Re ((z1z2)/( bar z1)) (ii) Im(1/(z1 bar...

    Text Solution

    |

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

    Text Solution

    |

  14. Find the real numbers x\ a n d\ y , if (x-i y)(3+5i) is the conjugate ...

    Text Solution

    |

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

    Text Solution

    |

  16. If (x+i y)^3=u+i v , then show that u/x+v/y=(x^2-y^2)dot

    Text Solution

    |

  17. If alphaand betaare different complex numbers with |beta|=1,then fin...

    Text Solution

    |

  18. Find the number of non-zero integral solution of the equation |1-i|^x=...

    Text Solution

    |

  19. If (a + i b) (c + i d) (e + if) (g + i h) = A + i B, then show that (a...

    Text Solution

    |

  20. If ((1+i)/(1-i))^m=1, then find the least integral value of m

    Text Solution

    |