Home
Class 12
MATHS
If z=(7-i)/(3-4i)" then "z^(14)=...

If `z=(7-i)/(3-4i)" then "z^(14)=`

A

`2^7`

B

`2^(7)i`

C

`2^(14)i`

D

`-2^(7)i`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NEW JOYTHI PUBLICATION|Exercise EXERCISE|50 Videos
  • BINOMIAL THEOREM

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|51 Videos
  • CONIC SECTIONS

    NEW JOYTHI PUBLICATION|Exercise EXERCISE - HYPERBOLA|9 Videos

Similar Questions

Explore conceptually related problems

If z=((1+i)/(1-i))^(9) find z+(1)/(z)

If z = (1)/((2 + 3i)^(2)) then |z| =

If z= e^((2pi i)/(3)) , then 1+z+3z^(2)+2z^(3)+2z^(4)+3z^(5) is equal to

If z=((1+i)(2+i))/((3+i)) find z^(-1) and barz .

If z_(1)=3+4i" and "z_(2)=2-i , verify that |z_(1)z_(2)|=|z_(1)||z_(2)| .

Let the complex numbers z_(1),z_(2),z_(3)" and "z_(4) denote the vertices of a square taken in order. If z_(1)=3+4i" and "z_(3)=5+6i , then the other two vertices z_(2)" and "z_(4) are respectively

If z=(-1)/(2)+i(sqrt(3))/(2), " then "8+10z+7z^(2) is equal to

If |(z-i)/(z+i)|=1 , then the locus of z is

If z=x+i ya n dw=(1-i z)//(z-i) , then show that |w|=1 z is purely real.

If z_(1)=3-4i , z_(2)=2+i find bar(z_(1)z_(2))

NEW JOYTHI PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTIONS FROM COMPETITIVE EXAMS
  1. i^(2)+i^(4)+i^(6)+"…………up to "(2k+1) terms, k in N is

    Text Solution

    |

  2. If z=sqrt(2)- isqrt(2) si rotated through an angle 45^(@) in the anti-...

    Text Solution

    |

  3. If z=(7-i)/(3-4i)" then "z^(14)=

    Text Solution

    |

  4. If (sqrt(8)+i)^(50)=3^(49)(a+ib)" then "a^(2)+b^(2) is

    Text Solution

    |

  5. If 3p^(2)=5p+2" and "3q^(2)= 5q+2, where p ne q, then the equation wh...

    Text Solution

    |

  6. If x=8+3sqrt(7)" and "xy=1, then the value of (1)/(x^2)+(1)/(y^2) is

    Text Solution

    |

  7. If alpha" and "beta, alpha" and "gamma" and "alpha" and "delta are the...

    Text Solution

    |

  8. The solution set of the equation pqx^(2)-(p+q)^(2)x+(p+q)^(2)=0 is

    Text Solution

    |

  9. If roots alpha, beta of the equation (x^(2)-bx)/(ax-c)=(lambda-1)/(lam...

    Text Solution

    |

  10. Let a= e^(i(2pi)/(3)). Then the equation whose roots are a+a^(-2)" and...

    Text Solution

    |

  11. If alpha(1), alpha(2), alpha(3), alpha(4) are the roots of the equatio...

    Text Solution

    |

  12. The roots of the eqaution (q-r)x^(2)+(r-p)x+(p-q)=0 are

    Text Solution

    |

  13. Let omega be a imaginary root of x^(n)=1. Then (5- omega)(5- omega^2)"...

    Text Solution

    |

  14. If isqrt(-1), then 4+5(-(1)/(2)+(isqrt(3))/(2))^(334)+3(-(1)/(2)+(isqr...

    Text Solution

    |

  15. If z is a complex number such that Re(z)=Im(z), then

    Text Solution

    |

  16. If alpha" and "beta are the roots of the equation x^(2)-7x+1=0, then t...

    Text Solution

    |

  17. If alpha " and "beta are different complex numbers with |beta|=1, then...

    Text Solution

    |

  18. If omega is a complex cube root of unity, then the value of sin{(omega...

    Text Solution

    |

  19. Let z=(11-3i)/(1+i). If alpha is a real number such z-ialpha is real, ...

    Text Solution

    |

  20. Let z(1)" and "z(2) be the roots of the equation z^(2)+pz+q=0, where p...

    Text Solution

    |