Home
Class 12
MATHS
Given z=f(x)+ig(x) where f,g:(0,1) to (0...

Given `z=f(x)+ig(x)` where `f,g:(0,1) to (0,1)` are real valued functions. Then which of the following does not hold good?

A

`z=1/(1-ix)+i(1/(1+ix))`

B

`z=1/(1+ix)+i(1/(1-ix))`

C

`z=1/(1+ix)+i(1/(1+ix))`

D

`z=1/(1-ix)+i(1/(1-ix))`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos
  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|11 Videos
  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise For Session 4|14 Videos
  • CIRCLE

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|16 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|20 Videos

Similar Questions

Explore conceptually related problems

Given f(x)={{:(3-[cot^(-1)((2x^3-3)/(x^2))], x >0) ,({x^2}cos(e^(1/x)) , x<0):} (where {} and [] denotes the fractional part and the integral part functions respectively). Then which of the following statements do/does not hold good?

Let f(x) is a real valued function defined by f(x)=x^(2)+x^(2) int_(-1)^(1) tf(t) dt+x^(3) int_(-1)^(1)f(t) dt then which of the following hold (s) good?

Consider f,g and h be three real valued differentiable functions defined on R. Let g(x)=x^(3)+g''(1)x^(2)+(3g'(1)-g''(1)-1)x+3g'(1) f(x)=xg(x)-12x+1 and f(x)=(h(x))^(2), where g(0)=1 Which one of the following does not hold good for y=h(x)

A differentiable function satisfies f(x) = underset(0) overset(x) int (f(t) cos t - cos(t - x))dt . Which of the following hold(s) good? a. f(x) has a minimem value 1-e b. f(x) has a maximum value 1-e^(-1) c. f''((pi)/(2))=e d. f'(0)=1

Let (dy)/(dx) + y = f(x) where y is a continuous function of x with y(0) = 1 and f(x) = {{:(e^(-x), if o le x le 2),(e^(-2),if x gt 2):} Which of the following hold(s) good ?

The function f is continuous and has the property f(f(x))=1-x for all x in [0,1] and J=int_0^1 f(x)dx . Then which of the following is/are true? (A) f(1/4)+f(3/4)=1 (B) f(1/3).f(2/3)=1 (C) the value of J equals to 1/2 (D) int_0^(pi/2) (sinxdx)/(sinx+cosx)^3 has the same value as J

Let f:[0,1]to[0,1] be a continuous function. Then prove that f(x)=x for at least one 0lt=xlt=1.

Let (f(x+y)-f(x))/(2)=(f(y)-1)/(2)+xy , for all x,y in R,f(x) is differentiable and f'(0)=1. Let g(x) be a derivable function at x=0 and follows the function rule g((x+y)/(k))=(g(x)+g(y))/(k), k in R,k ne 0,2 and g'(0)=lambda If the graphs of y=f(x) and y=g(x) intersect in coincident points then lambda can take values

Let f be a real valued function defined on the interval (0,oo) by f(x)=In x+int_(0)^(x)sqrt(1+sint)dt . Then which of the following statement (s) is (are) true?

ARIHANT MATHS-COMPLEX NUMBERS-Exercise (Single Option Correct Type Questions)
  1. If f(x)=g(x^(3))+xh(x^(3)) is divisiblel by x^(2)+x+1, then

    Text Solution

    |

  2. If the points represented by complex numbers z(1)=a+ib, z(2)=c+id " an...

    Text Solution

    |

  3. Let C and R denote the set of all complex numbers and all real numb...

    Text Solution

    |

  4. Let alpha and beta be two distinct complex numbers, such that abs(alph...

    Text Solution

    |

  5. The complex number z satisfies thc condition |z-25/z|=24. The maximum ...

    Text Solution

    |

  6. The points A,B and C represent the complex numbers z(1),z(2),(1-i)z(1)...

    Text Solution

    |

  7. Find the 6th term of A.P if a=1 , d=2

    Text Solution

    |

  8. Find the 3rd term of A.P if a=1 , d=2

    Text Solution

    |

  9. The centre of circle represented by |z + 1| = 2 |z - 1| in the complex...

    Text Solution

    |

  10. If x=9^(1/3) 9^(1/9) 9^(1/27) ......and if y= 4^(1/3) 4^(-1/9) 4^(1/...

    Text Solution

    |

  11. Find the 5th term of A.P if a=1 , d=2

    Text Solution

    |

  12. Let |Z(r) - r| le r, Aar = 1,2,3….,n. Then |sum(r=1)^(n)z(r)| is less ...

    Text Solution

    |

  13. If arg ((z(1) -(z)/(|z|))/((z)/(|z|))) = (pi)/(2) and |(z)/(|z|)-z(1)|...

    Text Solution

    |

  14. Find the 7th term of A.P if a=1 , d=2

    Text Solution

    |

  15. Find the 10th term of A.P if a=1 , d=2

    Text Solution

    |

  16. If z=(3+7i)(lambda+imu)," when " lambda,mu in I-{0} " and " i=sqrt(-1...

    Text Solution

    |

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

    Text Solution

    |

  18. If z^3+(3+2i)z+(-1+i a)=0 has one real roots, then the value of a lies...

    Text Solution

    |

  19. If m and n are the smallest positive integers satisfying the relation ...

    Text Solution

    |

  20. Number of imaginergy complex numbers satisfying the equation, z^(2)=ba...

    Text Solution

    |