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Number Theory T...

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  • Question 1
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    if $$\displaystyle\ z=1+i\ \tan \alpha $$, where $$\displaystyle\ \pi < \alpha < \frac{3\pi }{2}$$ is $$|z|$$ is equal to 

  • Question 2
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    For a complex number z, the minimum value of $$\displaystyle\ |z| + |z-2|$$ is 

  • Question 3
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    The value of the sum $$\displaystyle\ \sum _{n=1}^{13}\left ( i^{n}+i^{n+1} \right ) $$, where $$\displaystyle\ i=\sqrt{-1} $$

  • Question 4
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    The complex number which satisfies the equation $$z+\sqrt { 2 } \left| z+1 \right| +i=0$$ is

  • Question 5
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    If $$z$$ be a complex number, then the minimum value of $$\left | z-7 \right |+\left | z \right |$$ is

  • Question 6
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    If $$\displaystyle z= 1+i\sqrt{3}$$,then $$\displaystyle z^{6}$$ equals

  • Question 7
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    The locus of $$\displaystyle z= x+iy$$ which satisfying the inequality $$\displaystyle \log_{1/2}\left | z-1 \right |> \log_{1/2}\left | z-i \right |$$ is given by

  • Question 8
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    If$$\displaystyle\ z_{1}\neq-z_{2}$$ and $$\displaystyle\ |z_{1}+z_{2}|=\left | \frac{1}{z_{1}}+\frac{1}{z_{2}} \right |$$ then

  • Question 9
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    If $$\displaystyle z=1+i\cot\alpha,-\frac{\pi}{2}<\alpha<0,$$ then $$|z|$$ is equal to 

  • Question 10
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    If $$\displaystyle u_{i}=1-\frac{1}{i}$$ then $$\displaystyle u_{2}\cdot u_{3}\cdot ... \cdot u_{n}$$ is equal to 

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