Home
Class 12
MATHS
Let z be a non-zero complex number Then ...

Let z be a non-zero complex number Then what is `z^(-1)` (multiplicative inverse of z) equal to ?

A

`(vecz)/(|z|^(2))`

B

`(z)/(|z|^(2))`

C

`(vecz)/(|z|`

D

`(|z|)/(z)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let z be a non-zero complex number, such that `z=x+iywhere x, y in R`
Then `z^(-1)(1)/(x+iy)`
So, `z^(-1)(x-iy)/((x+iy)(x-iy))=(x-iy)/(x^(2)+y^(2))=(barz)/(|z|^(2))`
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    NDA PREVIOUS YEARS|Exercise MCQs|40 Videos

  • CONICS - PARABOLA, ELLIPSE & HYPERBOLA

    NDA PREVIOUS YEARS|Exercise MATH|62 Videos

Similar Questions

Explore conceptually related problems

If z is any non-zero complex number, prove that the multiplicative inverse of z is (overline(z))/(|z|^(2)) . Hence, express (4-sqrt(-9))^(-1) in the form x+iy, where x,y inR

Find the non-zero complex numbers z satisfying z=iz^(2)

Let z be any non-zero complex number. Then pr. arg(z) + pr.arg (barz) is equal to

If z= 4+ 7i be a complex number, then find (i) Additive inverser of z. (ii) Multiplicative inverse of z.

If z is a unimodular complex number then its multiplicative inverse is ( i) bar(z) (ii) z (iii) -z (iv) -bar(z)

Let a = Im((1+z^(2))/(2iz)) , where z is any non-zero complex number. Then the set A = {a : |z| = 1 and z ne +- 1} is equal to

Let a = Im((1+z^(2))/(2iz)) , where z is any non-zero complex number. Then the set A = {a : |z| = 1 and z ne +- 1} is equal to

A non-zero complex number z is uniquely determined if

Let z be a complex number satisfying |z+16|=4|z+1| . Then

NDA PREVIOUS YEARS-COMPLEX NUMBERS-Multiple choice question
  1. Let z=i^(3)(1+i) be a complex number. What is its argument ?

    Text Solution

    |

  2. Let z(1) and z(2) be two non-zero complex number such that |z(1)|=|z(...

    Text Solution

    |

  3. Let z be a non-zero complex number Then what is z^(-1) (multiplicative...

    Text Solution

    |

  4. Find all possible values of sqrt(i)+sqrt(-i)dot

    Text Solution

    |

  5. What is the value of [-1+isqrt3)//2]^(10)+[-1-isqrt3)//2]^(10)

    Text Solution

    |

  6. If omega denotes the cube root of unity, then what is the real root o...

    Text Solution

    |

  7. Let O be the origitn and point A be represented by z. If OA is rotated...

    Text Solution

    |

  8. If 1omega,omega^(2) are the three cube roots of unity, then what is ((...

    Text Solution

    |

  9. Find the square root of the following complex number: -5+12 i

    Text Solution

    |

  10. If alpha(1+isqrt3)/(2), then what is the value of 1+alpha^(8)+alpha^(1...

    Text Solution

    |

  11. A straight line is passing through thte points represented by the comp...

    Text Solution

    |

  12. Which one of the following is correct? Ifz and w are complex numbers a...

    Text Solution

    |

  13. What is the square root of 1/2-i(sqrt3)/(2)?

    Text Solution

    |

  14. Let C be the set of complex number and z(1),z(2) are in C. 1. agr (z...

    Text Solution

    |

  15. What is agr (bi) where b gt0 ?

    Text Solution

    |

  16. If omega is a complex non-real cube root of unity, then omega satisfie...

    Text Solution

    |

  17. For a positive integer n, what is the value of i^(4n+1) ?

    Text Solution

    |

  18. If omega is a complex cube root of unity, then what is the value of ...

    Text Solution

    |

  19. match List I which List II ans select the correct answer using to code...

    Text Solution

    |

  20. What is (sqrt3+i)//(1+sqrt3i) equal to ?

    Text Solution

    |