Home
Class 12
MATHS
Using De Moivre 's theorem prove that : ...

Using De Moivre 's theorem prove that :
`((1+cos theta +i sin theta)/(1+cos theta - i sin theta))^n= cos n theta + i sin n theta`, where `i = sqrt(-1)`

A

2

B

4

C

6

D

8

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise LEVEL - 2|50 Videos
  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise NUMRICAL VALUE TYPE FOR JEE MAIN|14 Videos
  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise JEE ARCHIVE|76 Videos
  • CIRCLES

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|68 Videos
  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

Similar Questions

Explore conceptually related problems

Prove that (cos^3 theta-sin^3 theta)/(cos theta-sin theta) = 1+cos theta sin theta

([cos theta+i sin theta)/(sin theta+i cos theta))^(4)=?

Prove that (1- cos theta + sin theta)/( 1+cos theta +sin theta) = "tan"(theta)/(2) .

Prove that : (cos theta)/(1-tan theta) + (sin theta)/(1-cot theta) = sin theta + cos theta

cos theta=sqrt(1-sin theta)

cos theta=sqrt(1-sin theta)

(sin theta + sin 2 theta)/( 1 + cos theta + cos 2 theta) = tan theta.

Prove that : (sin 5theta - 2 sin 3theta + sin theta)/(cos 5theta -cos theta) = tan theta

Prove that : (1+ sin theta - cos theta) / (1+ sin theta + cos theta ) = tan (theta/2)

Prove that : (sin theta + sin 3theta + sin 5theta)/(cos theta + cos 3theta + cos 5theta) = tan 3theta

VMC MODULES ENGLISH-COMPLEX NUMBERS -LEVEL - 1
  1. The argument of (1-isqrt(3))/(1+isqrt(3)) is 60^0 b. 120^0 c. 210^0 d....

    Text Solution

    |

  2. Evaluate: sqrt(-2+2sqrt(3)i)

    Text Solution

    |

  3. Using De Moivre 's theorem prove that : ((1+cos theta +i sin theta)/...

    Text Solution

    |

  4. Simplify: (sqrt(5+12 i)+sqrt(5-12 i))/(sqrt(5+12 i)-sqrt(5-12 i))

    Text Solution

    |

  5. If z1,z2 are two complex numbers such that Im(z1+z2)=0,Im(z1z2)=0, the...

    Text Solution

    |

  6. (1+2i+3i^2)/(1-2i+3i^2) equals i b. -i c. -1 d. 4

    Text Solution

    |

  7. If sqrt(3)+i=(a+i b)//(c+i d) , then find the value of tan^(-1)(b//a)t...

    Text Solution

    |

  8. If |z(1)|=|z(2)|andamp(z(1))+amp(z(2))=0, then

    Text Solution

    |

  9. If omega is a complex cube root of unity, then (1-omega+omega^(2))^(6...

    Text Solution

    |

  10. If omega(!= 1) be an imaginary cube root of unity and (1+omega^2)^n=(...

    Text Solution

    |

  11. Prove that x^(3p) + x^(3q+1) + x^(3r+2) is exactly divisible by x^2+x+...

    Text Solution

    |

  12. If z= x + yi and omega = ((1- zi))/(z-i), then |omega|=1 implies that ...

    Text Solution

    |

  13. The locus of z which satisfies the inequality log (0.3) abs(z-1) gt l...

    Text Solution

    |

  14. The set of points in an Argand diagram which satisfy both abs(z)le4 an...

    Text Solution

    |

  15. If the points represented by complex numbers z(1)=a+ib, z(2)=c+id " an...

    Text Solution

    |

  16. For x(1), x(2), y(1), y(2) in R if 0 lt x(1)lt x(2)lt y(1) = y(2)...

    Text Solution

    |

  17. If alpha,betaandgamma are the cube roots of P(p)lt0), then for any x, ...

    Text Solution

    |

  18. If z(1) , z(2), z(3) are three complex numbers in A.P., then they lie ...

    Text Solution

    |

  19. If the cube roots of unity are 1,omega,omega^2, then the roots of the ...

    Text Solution

    |

  20. about to only mathematics

    Text Solution

    |