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Number Theory T...

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  • Question 1
    1 / -0

    If $$a,b,c$$ are non-zero numbers and the equation $$ax^{2}+bx+c+i=0$$ has purely imaginary roots, then

  • Question 2
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    If the roots $$a^2x^2 +2bx+c^2 = 0$$ are imaginary then the roots of $$b(x^2+1)+2acx = 0$$ are 

  • Question 3
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    If $$z$$ is a complex number of unit modulus and argument $$\theta $$, then the real part of 
    $$\dfrac { z\left( 1-\bar { z }  \right)  }{ \bar { z } \left( 1+2 \right)  } $$ is:

  • Question 4
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    If $$a > b > c$$, $$a\neq 0$$ and the system of equations
    $$ax+by+cz=0$$, $$bx+cy+az=0$$, $$cx+ay+bz=0$$ has non-trivial solutions, then the roots of the quadratic equation $$at^2+bt+c=0$$.

  • Question 5
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    The value of $$(sin\frac{\pi }{8}+i\cos \frac{\pi }{8})^{8}{(sin\frac{\pi }{8}-i cos \frac{\pi }{8})^{8}}$$ is 

  • Question 6
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    The equation $$x(x+2)(x^{2}-x)=-1$$, has 

  • Question 7
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    If $$\overline { \Delta  } =\begin{vmatrix} -1 & 2-3i & 5+4i \\ 2+3i & 8 & 1-i \\ 5-4i & 1+i & 3 \end{vmatrix}$$ then $$\Delta =$$

  • Question 8
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    If $$\theta$$ real then the modulus of $$\dfrac{1}{1+\cos\theta+i\sin\theta}$$ is

  • Question 9
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    The function of imaginary roots of the equation $$(x-1)(x-2)(3x+1)=32$$ is 

  • Question 10
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    The number of imaginar roots of the equation $$(x-1)(x-2)(3x-2)(3x+1)=32$$ is

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