2000001502
Level:
A
Find the complex roots of the equation \(2x^2=-8\).
\( x_1 = 2i,~x_2=-2i\)
\( x_1 = x_2=2i\)
\( x_1 =x_2=-2i\)
The equation has no solution.
A
2000001501
Level:
A
Solve the quadratic equation \( x^2 +1 =0\) in the set of complex numbers.
\( x_{1,2} = \pm i\)
\( x_{1,2} = i\)
\( x_{1,2} = -i\)
\( x_{1,2} = \pm 1\)
2000001409
Level:
A
Find the vector \(\vec{c} = 2\vec{a} - \vec{b}\), where \(\vec{a}=(3,5) \) and \(\vec{b}=(-1,4) \).
\( (7,6) \)
\( (5,6) \)
\( (5,14) \)
\( (4,1) \)
2000001408
Level:
A
Find the vector \(\vec{c} = \vec{a} - \vec{b}\), where \(\vec{a}=(1,2) \) and \(\vec{b}=(-3,4) \).
\( (4,-2)\)
\( (-2,-2)\)
\( (4,2)\)
\( (2,-2)\)
2000001407
Level:
A
Find the vector \(\vec{c} = \vec{a} + 2\vec{b}\), where \(\vec{a}=(-1,3) \) and \(\vec{b}=(1,-2) \).
\( (1,-1) \)
\( (0,1) \)
\( (-1,4) \)
\( (1,7) \)
2000001406
Level:
A
Find the vector \(\vec{c} = 2\vec{a} + \vec{b}\), where \(\vec{a}=(2,3) \) and \(\vec{b}=(-2,5) \).
\((2,11)\)
\((0,8)\)
\((6,11)\)
\((6,8)\)
2000001405
Level:
A
Find the opposite vector of the vector \( (1,-3) \).
\( (-1,3) \)
\( (-3,1) \)
\( (3,1) \)
\( (1,3) \)
2000001404
Level:
A
Find the vector \(\overrightarrow{AB}\), where \(A=[-3,1]\) and \(B=[4,2]\).
\( (7,1) \)
\( (1,1) \)
\( (7,-1) \)
\( (-1,1) \)
2000001403
Level:
A
Find the vector \(\overrightarrow{AB}\), where \(A=[3,5]\) and \(B=[5,2]\).
\( (2,-3)\)
\((-2,3)\)
\((4,3.5)\)
\( (8,7)\)
2000001402
Level:
A
Find the length of the vector \((-5, 2)\).
\(\sqrt{29}\)
\(\sqrt{7}\)
\(\sqrt{3}\)
\(\sqrt{21}\)