Home
Class 11
MATHS
If x=(1+i)/sqrt2, prove that x^2 = i...

If `x=(1+i)/sqrt2`, prove that `x^2 = i`

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    A N EXCEL PUBLICATION|Exercise QUESTION BANK |106 Videos

  • CONIC SECTION

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|90 Videos

Similar Questions

Explore conceptually related problems

If x=(1+i)/sqrt2 .Prove that x^6+x^4+x^2+1=0

prove that (-1 + i)^2 = -2i

If y=sin^(-1)x/sqrt(1-x^2) prove that (1-x^2)y_1-xy=1

If y=sin^(-1)x/sqrt(1-x^2) prove that (1-x^2)y^2=(sin^(-1)x)^2

If y=sin^(-1)x/sqrt(1-x^2) prove that (1-x^2)y_2-3xy_1-y=0

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

If (a+i)^2/(2a-i) = p+iq , prove that p^2+q^2 = (a^2+1)^2/(4a^2+1)

If a+ib = sqrt((1+i)/(1-i)) , prove that a^2+b^2=1

A N EXCEL PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTION BANK
  1. Prove that abs((a+i)^2/(2a-i)) = (a^2+1)/(sqrt(4a^2+1))

    Text Solution

    |

  2. If (a+i)^2/(2a-i) = p+iq, prove that p^2+q^2 = (a^2+1)^2/(4a^2+1)

    Text Solution

    |

  3. If x=(1+i)/sqrt2, prove that x^2 = i

    Text Solution

    |

  4. If x=(1+i)/sqrt2.Prove that x^6+x^4+x^2+1=0

    Text Solution

    |

  5. Prove that abs((1+i)/(1-i)) = 1

    Text Solution

    |

  6. If a+ib = sqrt((1+i)/(1-i)), prove that a^2+b^2=1

    Text Solution

    |

  7. Prove that abs(costheta-isintheta) = 1

    Text Solution

    |

  8. If (costheta-isintheta)^2 = x -iy, show that x^2+y^2 = 1

    Text Solution

    |

  9. Complete the following table

    Text Solution

    |

  10. When two complex numbers are equal? Find the real values of x and y fo...

    Text Solution

    |

  11. Match the following

    Text Solution

    |

  12. Fill in the blanks by choosing the correct answer from the bracket ove...

    Text Solution

    |

  13. Suppose z1 = 1 - i and z2 = -2 + 4i Find z1z2

    Text Solution

    |

  14. Suppose z1 = 1 - i and z2 = -2 + 4i Find overlinez1

    Text Solution

    |

  15. Suppose z1 = 1 - i and z2 = -2 + 4i Find Im ((z1z2)/z1) and Re ((z1z2...

    Text Solution

    |

  16. Suppose z1 = 1 - i and z2 = -2 + 4i Joseph evaluted abs((z1z2)/z1) usi...

    Text Solution

    |

  17. Suppose z = x + iy and w = (1-iz)/(z-i) Find 1 - iz and z - 1 in the s...

    Text Solution

    |

  18. Suppose z = x + iy and w = (1-iz)/(z-i) Find absw. If absw = 1, prove...

    Text Solution

    |

  19. Consider the complex number z1 = 2 - i and z2 = -2 + i Find (z1z2)/z1...

    Text Solution

    |

  20. Consider the complex number z1 = 2 - i and z1 = -2 + i Raju prove tha...

    Text Solution

    |