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Number Theory T...

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  • Question 1
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    If$${ z }_{ 1 }$$ and $${ z }_{ 2 }$$ are two complex number such that Im$$({ z }_{ 1 }={ z }_{ 2 })$$= 0= Im $$({ z }_{ 1 }{ z }_{ 2 })$$, then 

  • Question 2
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    $$z$$ is a complex number. If $$a = | x | + | y |$$ and
    $$b = \sqrt { 2 } | x + i y |$$ then which of the following is
    true

  • Question 3
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    If $$z=(3+4i)^6+(3-4i)^6,$$ where $$i=\sqrt { -1 }, $$ then $$Im(z)$$ equals to 

  • Question 4
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    Number of complex numbers $$z$$ such that $$|z|=1$$ and $$\left|\dfrac {z}{z}+\dfrac {\bar {z}}{z}\right|=1$$ is

  • Question 5
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    The modulus of $$\dfrac { \left( 3+2i \right) ^{ 2 } }{ \left( 4-3i \right)  } $$ is:

  • Question 6
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    If a complex number z and $$z+\dfrac { 1 }{ z } $$ have same argument then- 

  • Question 7
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    A value of $$\theta $$ for which$$\dfrac { 2+3isin\theta  }{ 1-2isin\theta  } $$ is purely imaginary, is:

  • Question 8
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    If $$z$$ satisfies $$|z - 2+ 2i| \le 1$$

  • Question 9
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    If $$\dfrac { z+1 }{ z+i }$$ is purely imaginary, then z lies on a 

  • Question 10
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    Purely imaginary then find the sum of statement i $$a,b$$ 

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