Home
Class 12
MATHS
If z= re^(i theta)" then "|e^(iz)|=...

If `z= re^(i theta)" then "|e^(iz)|=`

A

`1`

B

`e^(2r sin theta)`

C

`e^(r sin theta)`

D

`e^(-r sin theta)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NEW JOYTHI PUBLICATION|Exercise EXERCISE|50 Videos
  • BINOMIAL THEOREM

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|51 Videos
  • CONIC SECTIONS

    NEW JOYTHI PUBLICATION|Exercise EXERCISE - HYPERBOLA|9 Videos

Similar Questions

Explore conceptually related problems

(1 + e^(-i theta))/(1 + e^(i theta)) =

If z=r(cos theta+ isin theta) , then the value of (z)/(bar z)+(barz)/(z) is

choose the correct pair of statement : (i) (costheta+isintheta)^(n)=cosntheta+isinntheta , x is an integer (ii) (sintheta+icostheta)^(n)=sinntheta+icosthetantheta , n is an integer (iii) If z=costheta+isintheta , then z^(-1)=costheta-isintheta (iv)(z+barz)/(2)=Re(z)

If z = (1)/(1 - cos theta - i sin theta), the Re (z)=

If z = 1 - cos theta + i sin theta , then |z| =

zo is one of the roots of the equation z^n cos theta0+ z^(n-1) cos theta2 +. . . . . . + z cos theta(n-1) + cos theta(n) = 2, where theta in R , then (A) |z0| 1/2 (C) |z0| = 1/2

If z= e^((2pi i)/(3)) , then 1+z+3z^(2)+2z^(3)+2z^(4)+3z^(5) is equal to

If z=i^(i^(i)) where i=sqrt-1 then |z| is equal to

The value of e^(I theta) - e^(-itheta) is …….

If z_(k)=e^(i theta_k) for k= 1, 2, 3, 4 where i^(2)= -1 , and if |sum_(k=1)^(4) (1)/(z_k)|=1 , then |sum_(k=1)^(4)| is equal to

NEW JOYTHI PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTIONS FROM COMPETITIVE EXAMS
  1. If alpha, beta are the roots of the equation (x-a)(x-b)=5 then the roo...

    Text Solution

    |

  2. If alpha, beta are roots of the equation ax^(2)+bx+c=0 then the value...

    Text Solution

    |

  3. If z= re^(i theta)" then "|e^(iz)|=

    Text Solution

    |

  4. i^(2)+i^(4)+i^(6)+"…………up to "(2k+1) terms, k in N is

    Text Solution

    |

  5. If z=sqrt(2)- isqrt(2) si rotated through an angle 45^(@) in the anti-...

    Text Solution

    |

  6. If z=(7-i)/(3-4i)" then "z^(14)=

    Text Solution

    |

  7. If (sqrt(8)+i)^(50)=3^(49)(a+ib)" then "a^(2)+b^(2) is

    Text Solution

    |

  8. If 3p^(2)=5p+2" and "3q^(2)= 5q+2, where p ne q, then the equation wh...

    Text Solution

    |

  9. If x=8+3sqrt(7)" and "xy=1, then the value of (1)/(x^2)+(1)/(y^2) is

    Text Solution

    |

  10. If alpha" and "beta, alpha" and "gamma" and "alpha" and "delta are the...

    Text Solution

    |

  11. The solution set of the equation pqx^(2)-(p+q)^(2)x+(p+q)^(2)=0 is

    Text Solution

    |

  12. If roots alpha, beta of the equation (x^(2)-bx)/(ax-c)=(lambda-1)/(lam...

    Text Solution

    |

  13. Let a= e^(i(2pi)/(3)). Then the equation whose roots are a+a^(-2)" and...

    Text Solution

    |

  14. If alpha(1), alpha(2), alpha(3), alpha(4) are the roots of the equatio...

    Text Solution

    |

  15. The roots of the eqaution (q-r)x^(2)+(r-p)x+(p-q)=0 are

    Text Solution

    |

  16. Let omega be a imaginary root of x^(n)=1. Then (5- omega)(5- omega^2)"...

    Text Solution

    |

  17. If isqrt(-1), then 4+5(-(1)/(2)+(isqrt(3))/(2))^(334)+3(-(1)/(2)+(isqr...

    Text Solution

    |

  18. If z is a complex number such that Re(z)=Im(z), then

    Text Solution

    |

  19. If alpha" and "beta are the roots of the equation x^(2)-7x+1=0, then t...

    Text Solution

    |

  20. If alpha " and "beta are different complex numbers with |beta|=1, then...

    Text Solution

    |