Home
Class 11
MATHS
If omega and omega^(2) are cube roots of...

If `omega and omega^(2)` are cube roots of unity, prove that `(2- omega + 2omega^(2)) (2 + 2omega- omega^(2))= 9`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    ICSE|Exercise Exercise (F )|28 Videos

  • COMPLEX NUMBER

    ICSE|Exercise MULTIPLE CHOICE QUESTIONS |34 Videos

  • COMPOUND AND MULTIPLE ANGLES

    ICSE|Exercise CHEPTER TEST |23 Videos

Similar Questions

Explore conceptually related problems

If 1, omega and omega^(2) are the cube roots of unity, prove that (a+b omega+c omega^(2))/(c+a omega+b omega^(2))=omega^(2)

If 1, omega, omega^(2) are three cube roots of unity, prove that (1 + omega - omega^(2)) (1- omega + omega^(2))=4

If 1, omega, omega^(2) are three cube roots of unity, prove that (1- omega) (1- omega^(2))= 3

If 1, omega, omega^(2) are three cube roots of unity, prove that (1+ omega- omega^(2))^(3)= (1- omega + omega^(2))^(3)= -8

If 1, omega, omega^(2) are three cube roots of unity, prove that (1- omega- omega^(2))^(6)= 64

Given that 1, omega, omega^(2) are cube roots of unity. Show that (1- omega + omega^(2))^(5) + (1 + omega - omega^(2))^(5)= 32

If, 1, omega, omega^(2) are cube roots of unity, show that (p + qomega + r omega^(2))/(r + p omega + q omega^(2))= omega^(2)

If 1, omega, omega^(2) are cube roots of unity, prove that (x + y)^(2) + (x omega + y omega^(2))^(2) + (x omega^(2) + y omega)^(2)= 6xy

If 1, omega, omega^(2) are three cube roots of unity, prove that (3+ 5omega + 3omega^(2))^(6) = (3 + 5omega^(2) + 3omega)^(6)= 64

If 1, omega, omega^(2) are three cube roots of unity, prove that omega^(28) + omega^(29) + 1= 0

ICSE-COMPLEX NUMBERS-Chapter Test
  1. Express (13i)/(2-3i) in the form A + Bi

    Text Solution

    |

  2. If z= x +yi and (|z-1-i|+4)/(3|z-1-i|-2)=1, show that x^(2) + y^(2) -2...

    Text Solution

    |

  3. If omega and omega^(2) are cube roots of unity, prove that (2- omega +...

    Text Solution

    |

  4. If z(1), z(2) in C (set of complex numbers), prove that |z(1) + z(2)| ...

    Text Solution

    |

  5. If z = x + yi, omega = (2-iz)/(2z-i) and |omega|=1, find the locus of ...

    Text Solution

    |

  6. Simplify: (1- 3omega + omega^(2)) (1 + omega- 3omega^(2))

    Text Solution

    |

  7. Find the locus of z satisfying |(z-3)/(z+1)|=3 in the complex plane.

    Text Solution

    |

  8. Given that (2 sqrt3 cos 30^(@) - 2i sin 30^(@))/(sqrt2 (cos 45^(@) + i...

    Text Solution

    |

  9. Simplify : (1- omega) (1- omega^(2)) (1- omega^(4)) (1- omega^(8))

    Text Solution

    |

  10. Find the locus of a complex number z= x + yi, satisfying the relation ...

    Text Solution

    |

  11. Find the real values of x and y satisfying the equality (x-2 + (y-3)i)...

    Text Solution

    |

  12. If i= (sqrt-1), prove that following (x+1+i) (x+ 1-i) (x-1-i) (x-1+ i)...

    Text Solution

    |

  13. If z= x + yi and |2z + 1| = |z- 2i|, show that 3(x^(2) + y^(2)) + 4(x-...

    Text Solution

    |

  14. Find the amplitude of the complex number "sin" (6pi)/(5) + i (1- "cos"...

    Text Solution

    |

  15. Express (1- 2i)/(2+i) + (3+i)/(2-i) in the form a + bi

    Text Solution

    |

  16. Find the value of x and y given that (x + yi) (2-3i)=4+i

    Text Solution

    |

  17. If the ratio (z-i)/(z-1) is purely imaginary, prove that the point z l...

    Text Solution

    |

  18. If (-2 + sqrt-3) (-3 + 2 sqrt-3) = a + bi, find the real numbers a and...

    Text Solution

    |

  19. If 1, omega, omega^(2) are the three cube roots of unity, then simplif...

    Text Solution

    |

  20. Find the locus of a complex number z= x+yi, satisfying the relation |3...

    Text Solution

    |