Home
Class 11
MATHS
Prove that : (i) sqrt(i)= (1+i)/(sqrt(...

Prove that : (i) `sqrt(i)= (1+i)/(sqrt(2))` (ii) `sqrt(-i)=(1- i)/(sqrt(2))` (iii) `sqrt(i)+sqrt(-i)=sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
N/a
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATION

    NAGEEN PRAKASHAN ENGLISH|Exercise EXERCISE 5C|14 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATION

    NAGEEN PRAKASHAN ENGLISH|Exercise EXERCISE 5D|6 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATION

    NAGEEN PRAKASHAN ENGLISH|Exercise EXERCISE 5A|9 Videos

  • BINOMIAL THEOREM

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exericse|20 Videos

  • CONIC SECTION

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|8 Videos

Similar Questions

Explore conceptually related problems

Rationalise the denominator of each of the following (i) (sqrt(3)+\ 1)/(sqrt(2)) (ii) (sqrt(2)+\ sqrt(5))/(sqrt(3)) (iii) (3sqrt(2))/(sqrt(5))

Find the value of :- (i) sqrt(4) (ii) sqrt(9) (iii) sqrt(16) (iv)sqrt(36)

If sqrt(2)=1.414,sqrt(3)=1.732 , find the value of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)" "(ii)(sqrt(3)-1)/(sqrt(3)+1)" "(iii)(2+sqrt(6))/(sqrt(2))

Simplify the following expressions: (i)\ (4+\ sqrt(7))\ (3+sqrt(2)) (ii)\ (3+sqrt(3))\ (5-sqrt(2)) (iii)\ (sqrt(5)-2)\ (sqrt(3)-sqrt(5))

Simplify the following expressions: (i) (4+sqrt(7))(3+sqrt(2)) (ii) (3+sqrt(3))(5-sqrt(2)) (iii) (sqrt(5)-2)(sqrt(3)-sqrt(5)) (iv) (sqrt(5)+sqrt(2))(sqrt(3)+sqrt(2))

Simplify the following expressions: (i)\ (11+sqrt(11))\ (11-\ sqrt(11)) (ii)\ (5+sqrt(7))(5-sqrt(7)) (iii)\ (sqrt(8)-sqrt(2))\ (sqrt(8)+\ sqrt(2))

Simplify : (i) (5+sqrt(5))(5-sqrt(5)) (ii) (3+2sqrt(2))(3-2sqrt(2))

Find the value of :- (i) (1)/(sqrt(4)) (ii) (1)/(sqrt(16)) (iii) (1)/(sqrt(64))

Simplify :- (i) (6)/(sqrt(2)) (ii) (sqrt(3))/(3) (iii) sqrt((3)/(4)) (iv) (6)/(sqrt(2)) (v) (sqrt(5))/(10) (vi) sqrt((16)/(2))

((1+i)/(sqrt(2)))^8+((1-i)/(sqrt(2)))^8 is equal to

NAGEEN PRAKASHAN ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATION -EXERCISE 5B
  1. Prove that ((-1+isqrt(3))/(2))^(3) is a positive integer.

    Text Solution

    |

  2. Convert [(3+2i)/( 3-2i)+ (3 -2i)/(3+2i)] in the form of (a+ib).

    Text Solution

    |

  3. Prove that : (i) sqrt(i)= (1+i)/(sqrt(2)) (ii) sqrt(-i)=(1- i)/(sqr...

    Text Solution

    |

  4. Find the sum and product of the complex number (3-4i) with its conjug...

    Text Solution

    |

  5. Find the sum and product of the complex number (-1 +2i) with its conj...

    Text Solution

    |

  6. Find the multiplicative inverse of the following complex number: (2+sq...

    Text Solution

    |

  7. Write the following in the form of ordered pair : (i) 3-2i (ii)...

    Text Solution

    |

  8. Convert the following in the form of a complex number : (i) (2, -5)...

    Text Solution

    |

  9. Find the values of x and y from the following : (i) (3x -7)+2iy=-5y+...

    Text Solution

    |

  10. If z=1+2i, show that z^(2)-2z+5=0. Hence find the value of z^(3) +7z^...

    Text Solution

    |

  11. Z=-5+4i then Z^4 +9Z^3 +35Z^2 – Z + 4 =

    Text Solution

    |

  12. If z(1)=2-i, z(2)=1+ 2i, then find the value of the following : (i)...

    Text Solution

    |

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

    Text Solution

    |

  14. (x+iy)^(1/3) =(a+ib) then prove that (x/a+y/b)=4(a^2-b^2)

    Text Solution

    |

  15. If ((a^(2)+1)^(2))/(2a-i) = a + iy , then what is the value of x^...

    Text Solution

    |

  16. Write the least positive integral value of n for which ((1+i)/(1-i))^n...

    Text Solution

    |

  17. The complex number z is purely imaginary , if

    Text Solution

    |

  18. A number of the form a + ib is called a complex number, where a,b in R...

    Text Solution

    |

  19. Find the real values of theta for which the complex number (1+i costhe...

    Text Solution

    |

  20. Find the square root of the following : (i) 3-4i (ii) 4+6isqrt(5) ...

    Text Solution

    |