Home
Class 12
MATHS
Let (-2 -1/3 i)^3=(x+iy)/27 (i= sqrt(-1)...

Let `(-2 -1/3 i)^3=(x+iy)/27 (i= sqrt(-1))` where x and y are real numbers then y-x equals

A

85

B

85

C

`-91`

D

91

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If 4x" "+" "i(3x-y)" "=" "3" "+" "i" "(-6) , where x and y are real numbers, then find the values of x and y.

(sqrt(x)+sqrt(y))^(2)=x+y+2sqrt(xy) and sqrt(x)sqrt(y)=sqrt(xy) , where x and y are positive real numbers . If a=1+sqrt(2)+sqrt(3) and b=1+sqrt(2)-sqrt(3) , then a^(2)+b^(2)-2a-2b=

Let A=[(x,y,z),(y,z,x),(z,x,y)] , where x, y and z are real numbers such that x + y + z > 0 and xyz = 2 . If A^(2) = I_(3) , then the value of x^(3)+y^(3)+z^(3) is__________.

If (3/2+(isqrt(3))/2)^(50)=3^(25)(x+iy) , where x and y are reals, then the ordered pair (x,y) is given by

The number of solutions of the equation (x^(4)+2x i)-(3x^(2)+iy)=(1+2yi)+(3-5i), where x and y are positive real is

Perform the indicated operation and give your anwer in the form x+iy , where x and y are real numbers and i=sqrt(-1) : (i) ((1)/(2)+(1)/(4)i)(-(2)/(3)-(1)/(4)i) (ii) (5+2i)/(-1+sqrt(3)i) . (iii) (sqrt(5)-7i)(sqrt(5)-7i)^(2)+(-2+7i)^(2) .

x+iy=(1-i sqrt(3))^(100), then (x,y)=

(a) Write the conjugates of the following: (i) 3+i (ii) 3-i (iii) -sqrt(5)-sqrt(7)i (iv) -sqrt(5)i (v) (4)/(5) (vi) 49-(i)/(7) (vii) (1-i)/(1+i) (viii) (1+i)^(2) (ix) (2+5i)^(2) (x) (-2-(1)/(3)i)^(3) (b) Find the real number x and y if: (i) (x-iy)(3+5i) is the conjugate of -6-24 i (ii) -3+ix^(2)y and x^(2)+y+4i are congugate of each other.

CENGAGE-JEE 2019-MCQ
  1. Let z(1) and z(2) be any two non-zero complex numbers such that 3|z(1)...

    Text Solution

    |

  2. If z=(sqrt(3)/2+i/2)^5+(sqrt(3)/2-i/2)^5 , then prove that Im(z)=0

    Text Solution

    |

  3. Let (-2 -1/3 i)^3=(x+iy)/27 (i= sqrt(-1)) where x and y are real numbe...

    Text Solution

    |

  4. Let (z-alpha)/(z+alpha) is purely imaginary and |z|=2, alphaepsilonR t...

    Text Solution

    |

  5. Let Z(1) and Z(2) be two complex numbers satisfying |Z(1)|=9 and |Z(2)...

    Text Solution

    |

  6. Consider the statement : " P(n) : n^(2)-n+41 is prime." Then, which on...

    Text Solution

    |

  7. If a ,b ,c are three distinct real numbers in G.P. and a+b+c=x b , the...

    Text Solution

    |

  8. Let a(1), a(2), ..., a(30) be an A. P., S = Sigma(i=10)^(30) a(1) and ...

    Text Solution

    |

  9. The sum of series 1+6+(9(1^(2)+2^(2)+3^(2)))/(7) + (12(1^(2)+2^(2)+...

    Text Solution

    |

  10. Let a, b and c be the 7th, 11th and 13th terms, respectively, of a non...

    Text Solution

    |

  11. The sum of all two-digit positive numbers which when divided by 7 yiel...

    Text Solution

    |

  12. If 5, 5r and 5r^(2) are the lengths of the sides of a triangle, then r...

    Text Solution

    |

  13. The sum of an infinite geometric series with positive terms is 3 and t...

    Text Solution

    |

  14. Let a1, a2, a3, ?a10 are in G.P. if a3/a1 =25 then a9/a5 is equal to ...

    Text Solution

    |

  15. If 19^(th) term of a non-zero A.P. is zero, then (49^(th) term) : (29^...

    Text Solution

    |

  16. The product of three consecutive terms of a GP is 512. If 4 is added t...

    Text Solution

    |

  17. Let S(k) = (1+2+3+...+k)/(k). If S(1)^(2) + s(2)^(2) +...+S(10)^(2) = ...

    Text Solution

    |

  18. If the sum of the first 15 terms of the series ((3)/(4))^(3)+(1(1)/(2)...

    Text Solution

    |

  19. Let x, y be positive real numbers and m, n be positive integers, The ...

    Text Solution

    |

  20. Consider a class of 5 girls and 7 boys. The number of different teams ...

    Text Solution

    |