Home
Class 12
MATHS
If the number of ordered pairs (a,b) whe...

If the number of ordered pairs `(a,b)` where `a,b in R` such that `(a+ib)^(5015)=(a-ib)^(3)` is `k`, then the unit digit of `k` is equal to________

Text Solution

Verified by Experts

The correct Answer is:
9
`a+ib=zimplies|z|^(5015)-|z|^(3)=0`
`|z|^(3)(|z|^(5012)-1)=0`
`|z|=0` or `|z|^(5012)=1implies|z|implieszbarz=1`
`z=0`
`z^(5015)=barz^(3)=z^(5015)=1/(z^(3))impliesz^(5018)=1`
Number of complex numbers `=5018+1=5019`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE

    FIITJEE|Exercise NUMERICAL BASED|4 Videos

  • TIPS

    FIITJEE|Exercise NUERICAL DECIMAL BASED QUATIONS|20 Videos

Similar Questions

Explore conceptually related problems

Number of ordered pairs (s) , (a,b) of real numbers such that (a+ib)^(2008)=a-ib holds good is

The number of ordered pairs (r, k) for which 6(""^(35)C_(r))=(k^(2)-3)(""^(36)C_(r+1)) , where k is an integer, is:

Write the order pair (2,-3) in the form of (a+ib) .

If 13 e^(i tan^(-1)(5//12))= a+ib , then |a| + |b| is equal to ____________.

a,b in R, find the number of complex numbers a+ib for which (a+ib)^(2)=(a-ib)^(2)

If A is an invertible matrix of order 3 and B is another matrix of the same order as of A, such that |B|=2, A^(T)|A|B=A|B|B^(T). If |AB^(-1)adj(A^(T)B)^(-1)|=K , then the value of 4K is equal to

If x, y, a, b are real numbers such that (x+iy)^(1//5)=a + ib and p = (x)/(a) - (y)/(b) , then

If (x+iy)^((1)/(3))=a+ib where x,y,a,b are real numbers such that (x)/(a)-(y)/(b)=k(a^(2)+b^(2)) then the value of k is

FIITJEE-TEST PAPERS-MATHEMATICS
  1. If a=1+x^3/(3!)+x^6/(6!)+.....oo, b=x+x^4/(4!)+x^7/(7!)+.....oo , c=...

    Text Solution

    |

  2. Let A=[(l,m,n),(p,q,r),(1,1,1)] and B=A^(2). If (l-m)^(2)+(p-q)^(2)=9,...

    Text Solution

    |

  3. If the number of ordered pairs (a,b) where a,b in R such that (a+ib)^(...

    Text Solution

    |

  4. A is a matrix of 3xx3 and a(ij) is its elements of i^(th) row and j^(t...

    Text Solution

    |

  5. If x and y satisfy te equation xy-2x^(2)-9x+3y-16=0 then

    Text Solution

    |

  6. Let p, q be integers and let alpha,beta be the roots of the equation ...

    Text Solution

    |

  7. For any two positive integers x and y f(x,y)=1/((x+1)!)+1/((x+2)!)+1/(...

    Text Solution

    |

  8. Let agt0, bgt0, cgt0 and a+b+c=6 then ((ab+1)^(2))/(b^(2))+((bc+1)^(2)...

    Text Solution

    |

  9. A and B play a game in which they alternately call out positive intege...

    Text Solution

    |

  10. Which of the following is/are correct?

    Text Solution

    |

  11. Consider all 10 digit numbers formed by using all the digits 0, 1, 2, ...

    Text Solution

    |

  12. Let A(z(1)), B(z(2)), C(z(3) and D(z(4)) be the vertices of a trepeziu...

    Text Solution

    |

  13. Let A(z(1)), B(z(2)), C(z(3) and D(z(4)) be the vertices of a trepeziu...

    Text Solution

    |

  14. In the equation A+B+C+D+E=FG. Where FG is the two digit number whose v...

    Text Solution

    |

  15. In the equation A+B+C+D+E=FG. Where FG is the two digit number whose v...

    Text Solution

    |

  16. If a,b,c are three positive real numbers then the minimum value of (a+...

    Text Solution

    |

  17. If the quadratic equation a(1)x^(2)-a-(2)x+a(3)=0 where a(1),a(2),a(3)...

    Text Solution

    |

  18. Let a(1),a(2),a(3),a(4),a(5) be a five term geometric sequence satisfi...

    Text Solution

    |

  19. If the coefficient of x^((n^(2)+n-18)/2) in (x-1)(x^(2)-2)(x^(3)-3)(x^...

    Text Solution

    |

  20. If a,b,c are three positive numbers then the minimum value of (a^(4)+b...

    Text Solution

    |