2000002101 Level: AFind the algebraic form of the complex number \( \left((\sqrt[3]{4}(\cos{\frac{\pi}{6}}+i\sin{\frac{\pi}{6}})\right)^3 \).\( 4i\)\( -4i \)\( 4 \)\( 4\left(\frac{\sqrt{3}}{2} + \frac{1}{2}i\right)\)
2000001904 Level: AThe picture shows the graphical solution of an equation. Which equation is it?\[ \sin{x} = -\frac{1}{2} \] \[ x \in [ 0;2\pi ]\]\[ \sin{x} = -\frac{\sqrt{3}}{2} \] \[ x \in [ 0;2\pi ]\]\[ \cos{x} = -\frac{1}{2} \] \[ x \in [ 0;2\pi ]\]\[ \cos{x} = -\frac{\sqrt{3}}{2} \] \[ x \in [ 0;2\pi ]\]
2000001903 Level: AThe picture shows the graphical solution of an equation. Which equation is it?\[ \sin{x} = -\frac{\sqrt{3}}{2} \] \[ x \in [ 0;2\pi ]\]\[ \sin{x} = -\frac{1}{2} \] \[ x \in [ 0;2\pi ]\]\[ \cos{x} = -\frac{\sqrt{3}}{2} \] \[ x \in [ 0;2\pi ]\]\[ \cos{x} = -\frac{1}{2} \] \[ x \in [ 0;2\pi ]\]
2000001902 Level: AThe picture shows the graphical solution of an equation. Which equation is it?\[ \cos{x} = -\frac{\sqrt{3}}{2}\] \[ x \in [ 0; 2\pi ] \]\[ \sin{x} = -\frac{\sqrt{3}}{2}\] \[ x \in [ 0; 2\pi ] \]\[ \sin{x} = -\frac{1}{2}\] \[ x \in [ 0; 2\pi ] \]\[ \cos{x} = -\frac{1}{2}\] \[ x \in [ 0; 2\pi ] \]
2000001901 Level: AThe picture shows the graphical solution of an equation. Which equation is it?\[ \cos{x} = -\frac{1}{2} \] \[ x \in [ 0;2\pi ]\]\[ \sin{x} = -\frac{1}{2} \] \[ x \in [ 0;2\pi ]\]\[ \cos{x} = -\frac{\sqrt{3}}{2} \] \[ x \in [ 0;2\pi ]\]\[ \sin{x} = -\frac{\sqrt{3}}{2} \] \[ x \in [ 0;2\pi ]\]
2000001512 Level: ALet \( x_1=2-\frac{\sqrt{5}}{2}i\) be one of the roots of a quadratic equation with real coefficients. Find the other root \(x_2\) of this equation.\( x_2 =2+\frac{\sqrt{5}}{2}i\)\( x_2 =-2-\frac{\sqrt{5}}{2}i\)\( x_2 =-2+\frac{\sqrt{5}}{2}i\)\( x_2 = \frac{1}{2-\frac{\sqrt{5}}{2}i}\)
2000001509 Level: AFind the right formula for solving the equation \(2x^2+5x+5=0\).\( x_{1,2}=\frac{-5\pm i\sqrt{15}}{4} \)\( x_{1,2}=\frac{5\pm i\sqrt{15}}{4} \)\( x_{1,2}=\frac{-5\pm i\sqrt{15}}{2} \)\( x_{1,2}=\frac{-5i\pm i\sqrt{40}}{4} \)
2000001506 Level: AFactorize the equation \(4x^2+25=0\) in the set of complex numbers.\( 4\left( x-\frac{5}{2}i\right)\left( x+\frac{5}{2}i\right)=0\)\(( 2x+5)( 2x+5)=0\)\( 4\left( x+\frac{5}{2}i\right)\left( x+\frac{5}{2}i\right)=0\)\( 4\left( x-\frac{5}{2}i\right)\left( x-\frac{5}{2}i\right)=0\)
2000001504 Level: AFind the product of the complex roots of the equation \(x^2 = -25\).\( 25 \)\( -25i\)\( -25\)\( 25i\)
2000001503 Level: AFind the sum of the complex roots of the equation \(3x^2 +27=0\).\( 0\)\( 6\)\( -6i\)\( 6i\)