Self Studies

Number Theory T...

TIME LEFT -
  • Question 1
    1 / -0

    If $${z}_{1},{z}_{2},..{z}_{n}$$ lie on the circle $$|z|=2$$ then the value of $$|{z}_{1},{z}_{2},..{z}_{n}|-4|\dfrac {1}{{z}_{1}}+\dfrac {1}{{z}_{2}}++\dfrac {1}{{z}_{n}}|=$$

  • Question 2
    1 / -0

    What is $${ i }^{ 1000 }+{ i }^{ 1001 }+{ i }^{ 1002 }+{ i }^{ 1003 }$$ equal to (where $$i=\sqrt { -1 } $$)?

  • Question 3
    1 / -0

    If $$\sqrt{3}+i(a+ib)(c+id)$$, then $$\tan^{-1}\left(\dfrac{b}{a}\right)+\tan^{-1}\left(\dfrac{d}{c}\right)$$ has the value

  • Question 4
    1 / -0

    If $$Z_{1},Z_{2}$$ are two complex numbers satisfying $$|\dfrac{Z_{1}-3Z_{2}}{3-Z_{1}Z_{2}}|=1|z_{1}|\neq 3$$ then $$|z_{2}|=$$

  • Question 5
    1 / -0

    A complex number z is said to be unimodular if $$|z| =1. $$. Suppose $$z_1$$ and $$z_2$$ are complex numbers such that $$\frac{z_1-2z_2}{2-z_1\overline {z}_2}$$ is unimolecolar and $$z_2$$ is not unimodular. Then the point $$z_1$$ lies on a:

  • Question 6
    1 / -0

    For $${ { Z }_{ 1 }=\sqrt [ 6 ]{ \dfrac { 1-i }{ 1+i\sqrt { 3 }  }  }  };\quad { { Z }_{ 2 }=\sqrt [ 6 ]{ \dfrac { 1-i }{ \sqrt { 3 } +i }  } ;\quad { { Z }_{ 3 }=\sqrt [ 6 ]{ \dfrac { 1-i }{ \sqrt { 3 } -i }  }  } }$$ which of the following holds good?

  • Question 7
    1 / -0

    The value of $$(z+3) (\overline{z} +3)$$ is eqquivalent to

  • Question 8
    1 / -0

    The imaginary part of $$(z - 1)(\cos \, \alpha - i \, \sin \, \alpha) + (z - 1)^{-1} \times (\cos \, \alpha + i \, \sin \, \alpha ) $$ is zero, if 

  • Question 9
    1 / -0

    If $$\left| z \right| \ge 5$$ then the least value $$\left| {z + \frac{2}{z}} \right|$$ is 

  • Question 10
    1 / -0

    For a complex number $$z$$, the minimum value of $$\left | z \right |+\left | z-\cos\alpha-i\sin\alpha \right |$$ is

Submit Test
Self Studies
User
Question Analysis
  • Answered - 0

  • Unanswered - 10

  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10
Submit Test
Self Studies Get latest Exam Updates
& Study Material Alerts!
No, Thanks
Self Studies
Click on Allow to receive notifications
Allow Notification
Self Studies
Self Studies Self Studies
To enable notifications follow this 2 steps:
  • First Click on Secure Icon Self Studies
  • Second click on the toggle icon
Allow Notification
Get latest Exam Updates & FREE Study Material Alerts!
Self Studies ×
Open Now