Home
Class 12
MATHS
If the complex numbers xa n dy satisfy x...

If the complex numbers `xa n dy` satisfy `x^3-y^3=98 ia n dx-y=7i ,t h e nx y=a+i b ,w h e r ea ,b , in Rdot` The value of `(a+b)//3` equals ______.

Text Solution

Verified by Experts

The correct Answer is:
21
We have
`x^(3) - y^(3) = 98i`
` or (x-y) ^(3) + 3xy(x-y) = 98i`
` or -343i+ 3(a+ib)(7i) = 98i`
`or -343 + 3(a+bi) 7 =98`
`or a+ib =21`
`rArr a = 21 and b=0`
`rArr a+b =21`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE|Exercise JEE Main Previous Year|11 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise MATRIX MATCH TYPE|9 Videos

  • CIRCLES

    CENGAGE|Exercise Question Bank|32 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|91 Videos

Similar Questions

Explore conceptually related problems

If the complex numbers x and y satisfy x^(3)-y^(3)=98i and x-y=7i ,then xy=a+ib, where a,b,in R The value of (a+b)/3 equals

IfI_n=int_x^pix^nsinx dx ,t h e n fin d t h e v a l u eof I_5+20 I_3dot

If the complex number omega=x+iy(AA x, y in R and i^(2)=-1) satisfy the equation omega^(3)=8i , then the maximum vlaue of y is

Let a , b ,xa n dy be real numbers such that a-b=1a n dy!=0. If the complex number z=x+i y satisfies I m((a z+b)/(z+1))=y , then which of the following is (are) possible value9s) of x? (a)-1-sqrt(1-y^2) (b) 1+sqrt(1+y^2) (c)-1+sqrt(1-y^2) (d) -1-sqrt(1+y^2)

If x^(a)y^(b)=(x-y)^(a+b) , then the value of (dy)/(dx)-(y)/(x) is equal to

If x , y >0,(log)_y x+(log)_x y=(10)/3 a n d x y=144 , t h e n(x+y)/2=sqrt("N")" w h e r e N" is a natural number, find the value of Ndot

If x=1/3y a n d y=1/2, t h e n x : y : z is equal to 1:2:6 b. 1:3:6 c. 2:4:6 d. 3:2:1

y=x^3e^x then, dy/dx=?

If a,x,b are in H.P. And a,y,z,b are in G.P.,then the value of (yz)/(x(y^3+z^3)) is

CENGAGE-COMPLEX NUMBERS-Exercise (Numerical)
  1. If x=a+b i is a complex number such that x^2=3+4ia d nx^3=2+1i ,w h e ...

    Text Solution

    |

  2. If the complex numbers xa n dy satisfy x^3-y^3=98 ia n dx-y=7i ,t h e ...

    Text Solution

    |

  3. If x=omega-omega^2-2 then , the value of x^4+3x^3+2x^2-11x-6 is (where...

    Text Solution

    |

  4. Let z=9+b i ,w h e r eb is nonzero real and i^2=-1. If the imaginary p...

    Text Solution

    |

  5. Modulus of nonzero complex number z satifying barz + z =0 and |z|^(2)-...

    Text Solution

    |

  6. If the expression (1 + ir)^3 is of the form of s(1+ i) for some real '...

    Text Solution

    |

  7. If complex number z(z!=2) satisfies the equation z^2=4z+|z|^2+(16)/(|z...

    Text Solution

    |

  8. The complex number z satisfies z+|z|=2+8i. find the value of |z|-8

    Text Solution

    |

  9. Let |z|=2a n dw-(z+1)/(z-1),w h e r ez ,w , in C (where C is the set ...

    Text Solution

    |

  10. If z is a complex number satisfying z^4+z^3+2z^2+z+1=0 then the set of...

    Text Solution

    |

  11. Let 1, omega,omega^(2) be the cube roots of unity. The least possib...

    Text Solution

    |

  12. If omega is the imaginary cube roots of unity, then the number of p...

    Text Solution

    |

  13. Suppose that z is a complex number the satisfies |z-2-2i|lt=1. The max...

    Text Solution

    |

  14. If |z+2-i|=5 and maxium value of |3z +9-7i| is M, then the value of M ...

    Text Solution

    |

  15. Let Z1 = (8 + i)sin theta + (7 + 4i)cos theta and Z2 = (1 + 8i)sin th...

    Text Solution

    |

  16. Let A={a in R} the equation (1+2i)x^3-2(3+i)x^2+(5-4i)x+a^2=0 has at ...

    Text Solution

    |

  17. Find the minimum value of the expression E= |z|^2+ |z-3|^2 + |z- 6i|^2...

    Text Solution

    |

  18. If z1 lies on |z-3| + |z + 3| = 8 such that arg z1 = pi//6 , ...

    Text Solution

    |

  19. If z satisfies the condition arg(z + i) = (pi)/(4) . Then the ...

    Text Solution

    |

  20. Let omega ne 1 be a complex cube root of unity. If ( 4 + ...

    Text Solution

    |