Home
Class 11
MATHS
If x=1+i is a root of the equation =x^3-...

If `x=1+i` is a root of the equation `=x^3-i x+1-i=0,` then the other real root is `0` b. `1` c. `-1` d. none of these

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos
  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

If x = 1 + i is a root of the equation x^(2) - ix - 1-i = 0 then the other real root is

IF 3+i is a root of the equation x^2 + ax + b=0 then a=

If (1 + i sqrt(3))/(2) is a root of the equation x^4-x^3 +x-1=0 then its real roots are

For the equation |x^2|+|x|-6=0 , the sum of the real roots is (a) 1 (b) 0 (c) 2 (d) none of these

If one root of the equation 2x^2+k x-6=0 is 2, then the other root is (a) 6 (b) -6 (c) -1 (d) 1

Find the roots of the equation x^(2) + ix - 1 - i = 0

If 1 - I is a root of the equation x^(2) + ax +b = 0 where a b in R then value of a is

If one root of the equation i x ^2 - 2(1+i) x+ (2-i) =0 is 2- I then the root is

If one root of the equation x^2+a x+3=0 is 1, then the other root is (a) 3 (b) -3 (c) 2 (d) -2

Number of real roots of the equation e^(x-1)-x=0 is

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If z1, z2a n dz3, z4 are two pairs of conjugate complex numbers, then ...

    Text Solution

    |

  2. Prove that following inequalities: |z/(|z|)-1|lt=|a rgz| (ii) |z-1|lt=...

    Text Solution

    |

  3. If x=1+i is a root of the equation =x^3-i x+1-i=0, then the other real...

    Text Solution

    |

  4. Find the modulus, argument, and the principal argument of the complex ...

    Text Solution

    |

  5. Find the principal argument of the complex number ((1+i)^5(1+sqrt(3i))...

    Text Solution

    |

  6. Column I, Column II: possible argument of z=a+i b a b >0 , p. tan^(...

    Text Solution

    |

  7. If the expression x^2+2(a+b+c)+3(b c+c+a b) is a perfect square, then ...

    Text Solution

    |

  8. Find the point of intersection of the curves a r g(z-3i)=(3pi)/4a n d ...

    Text Solution

    |

  9. The curve y=(lambda+1)x^2+2 intersects the curve y=lambdax+3 in exac...

    Text Solution

    |

  10. Column I, Column II (one of the values of z ) z^4-1=0 , p. z=cospi/...

    Text Solution

    |

  11. Let za n dw be two nonzero complex numbers such that |z|=|w|a n d arg...

    Text Solution

    |

  12. The number of irrational roots of the equation (4x)/(x^2+x+3)+(5x)/(x^...

    Text Solution

    |

  13. If |z+barz|+|z-barz|=2 then z lies on (a) a straight line (b) a set of...

    Text Solution

    |

  14. If one vertex of the triangle having maximum area that can be inscribe...

    Text Solution

    |

  15. The number of complex numbers z satisfying |z-3-i|=|z-9-i|a n d|z-3+3i...

    Text Solution

    |

  16. If the equation x^2-3p x+2q=0a n dx^2-3a x+2b=0 have a common roots a...

    Text Solution

    |

  17. Solve the equation 3^(x^2-x)+4^(x^2-x)=25.

    Text Solution

    |

  18. If t and c are two complex numbers such that |t|!=|c|,|t|=1a n dz=(a t...

    Text Solution

    |

  19. Consider the circle |z|=r in the Argand plane, which is in fact the in...

    Text Solution

    |

  20. Solve the equation 12x^4-56 x^3+89 x^2-56 x+12=0.

    Text Solution

    |