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 \((-5; 2)\).
\(\sqrt{29}\)
\(\sqrt{7}\)
\(\sqrt{3}\)
\(\sqrt{21}\)