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Number Theory T...

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  • Question 1
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     lf $$Z=x+iy$$ is a complex number then $$|x|+|y|\leq$$ ?

  • Question 2
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    Statement 1: Let z be a complex number, then the equation $$z^4+z+2=0$$ cannot have a root, such that $$|z| < 1$$.
    Statement 2: $$|z_1+z_2| \leq |z_1|+|z_2|$$

  • Question 3
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    If z is unimodular complex number then $$\mathrm{z}= (\displaystyle \frac{1+ia}{1-ia})^{4}$$ has

  • Question 4
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    lf $$z_{1},\ z_{2}$$ are any two complex numbers then $$\left |z_{1^{+}}\sqrt{\mathrm{z}_{1}^{2}-\mathrm{z}_{2}^{2}} \right |+\left|\mathrm{z}_{1}-\sqrt{\mathrm{z}_{1}^{2}-\mathrm{z}_{2}^{2}} \right|$$ is equal to

  • Question 5
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    If $$\dfrac{x+3i}{2+iy}=1-i$$, then the value of $$\left ( 5x-7y \right )^2$$ is

  • Question 6
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    $$\mathrm{l}\mathrm{n}$$ a G. $$\mathrm{P}$$ first term is $$\sqrt{3}+i$$ and common ratio is $$\sqrt{3}-i$$ then the modulus of the $$n^{th}$$ term of the G.$$\mathrm{P}$$. is

  • Question 7
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    If $$\alpha,\ \beta,\ \gamma$$ are modulus of the complex number $$3+4i, -5+12i,\ 1-i$$, then the increasing order for $$\alpha, \beta $$ and $$\gamma$$ is

  • Question 8
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    If $$|\mathrm{z}-4|<|\mathrm{z}-2|$$, its solution is given by

  • Question 9
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    Solve the equation $$\left|z\right| = z + 1 + 2i$$.

  • Question 10
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    If $$z = x + iy$$ and $$w = \displaystyle \frac{1 - zi}{z - i}, |w| = 1$$, then find the locus of z.

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