Home
Class 12
MATHS
about to only mathematics...

about to only mathematics

A

`z',z'.z''` are in G.P

B

z',z',z'' are H.P

C

`z'+z'' = 2z cos alpha `

D

`z'^(2)+z''^(2) = 2z^(2) cos 2alpha`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`z'=ze^(ialpha)" "(1)`
`z'' = ze^(-ialpha)" "(2)`
`therefore z'z''= z^(2)`
`rArr z',z,z'' ` are in G.P
Also , `((z)/(z))^(2) + ((z'')/(z)) = 2cos alpha `
`z'^(2) + z''^(2) = 2z^(2) cos 2 alpha`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise LINKED COMPREHENSION TYPE|36 Videos

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise NUMERICAL VALUE TYPES|33 Videos

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise single correct Answer type|92 Videos

  • CIRCLES

    CENGAGE ENGLISH|Exercise Comprehension Type|8 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|101 Videos

Similar Questions

Explore conceptually related problems

In a certain collage, the ratio of mathematics majors to English majors is 3:8. If in the following school year the number of mathematics majors increase 20%, and the number of English majors decrease 15%, what is the new ratio of mathematics majors to English majors?

STATEMENT-1 : Magnetic poles are only mathematical assumptions and have no real existence . and STATEMENT-2 : Magnetic field lines are always in closed loops .

72% of 25 students are good in mathematics. How many are not good in mathematics?

in a class of 35 students , 17 have taken Mathematics , 10 have taken mathematics but not economics if each student has taken erither mathematics Of Economics or both , then the number of students who have taken Economics but not mathematics is

Rahim obtained 60 marks out of 75 in Mathematics. Find the percentage of marks obtained by Rahim in Mathematics.

There are five books on Mathematics and 6 books on Physics in a book shop. In how many ways can a student buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?

A bag contains a total of 20 books on physics and mathematics. Ten books are chosen from the bag and it is found that it contains 6 books of mathematics. Find out the probability that the remaining books in the bag contains 2 books on mathematics.

From 50 students taking examinations in mathematics, physics and chemistry,37 passed mathematics, 24 physics and 43 chemistry. At most 19 passed mathematics and physics, at most 29 mathematics and chemistry and at most 20 physics and chemistry. Find the largest possible number that could have passed all three exams.

From 50 students taking examinations in mathematics, physics and chemistry,37 passed mathematics, 24 physics and 43 chemistry. At most 19 passed mathematics and physics, at most 29 mathematics and chemistry and at most 20 physics and chemistry. Find the largest possible number that could have passed all three exams.

check whether it is statement or not .Do you like mathematics ?

CENGAGE ENGLISH-COMPLEX NUMBERS-MULTIPLE CORRECT ANSWERS TYPE
  1. System of equaitons |z+3|-|z-3| = 6 and |z-4|=r where r in R^(+) has

    Text Solution

    |

  2. Let the equation of a ray be |z-2|-|z-1-i| = sqrt(2). If it strikes t...

    Text Solution

    |

  3. Given that the two curves a r g(z)=pi/6 and |z-2sqrt(3)i|=r intersect ...

    Text Solution

    |

  4. On the Argand plane ,let z(1) = - 2+ 3z,z(2)= - 2-3z and |z| = 1. T...

    Text Solution

    |

  5. Let S = { z: x = x+ iy, y ge 0,|z-z(0)| le 1}, where |z(0)|= |z(0) - o...

    Text Solution

    |

  6. If P and Q are represented by the complex numbers z(1) and z(2) such ...

    Text Solution

    |

  7. Locus of complex number satisfying "a r g"[(z-5+4i)//(z+3-2i)]=pi//4 i...

    Text Solution

    |

  8. Equation of tangent drawn to circle abs(z)=r at the point A(z(0)), is

    Text Solution

    |

  9. If n is a natural number gt 2, such that z^(n) = (z+1)^(n), then (a) ...

    Text Solution

    |

  10. If |z-(1/z)|=1, then a. (|z|)(m a x)=(1+sqrt(5))/2 b. (|z|)(m in)=(s...

    Text Solution

    |

  11. about to only mathematics

    Text Solution

    |

  12. Let z be a complex number satisfying equation z^p-z^(-q)=0,\ where\ p ...

    Text Solution

    |

  13. Which of the following is true ?

    Text Solution

    |

  14. about to only mathematics

    Text Solution

    |

  15. about to only mathematics

    Text Solution

    |

  16. z(1),z(2),z(3) and z'(1),z'(2),z'(3) are nonzero complex numbers such...

    Text Solution

    |

  17. Given z=f(x)+ig(x) where f,g:(0,1) to (0,1) are real valued functions....

    Text Solution

    |

  18. Let a, b, c be distinct complex numbers with |a|=|b|=|c|=1 and z(1), z...

    Text Solution

    |

  19. If all the three roots of az^(3)+bz^(2)+cz+d=0 have negative real part...

    Text Solution

    |

  20. If (3)/(2+e^(itheta)) =ax + iby, then the locous of P(x,y) will repre...

    Text Solution

    |