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9000032011

Level:

Evaluate

tg (\frac{π}{3})

\sqrt{3}

0

- \sqrt{3}

- \frac{\sqrt{3}}{3}

- \frac{\sqrt{2}}{2}

\frac{\sqrt{3}}{3}

9000032114

Level:

Evaluate

\cos (\frac{π}{6})

\frac{\sqrt{3}}{2}

\frac{\sqrt{2}}{2}

- \frac{1}{2}

- \frac{\sqrt{3}}{2}

0

- \frac{\sqrt{2}}{2}

9000031202

Level:

Find the imaginary part of the complex number

z = \frac{2 + i}{1 - i}

\frac{3}{2}

- \frac{3}{2}

\frac{1}{2}

- \frac{1}{2}

9000031204

Level:

Find the absolute value of the complex number

z = \frac{2 - i}{2 + i}

1

5

\frac{\sqrt{7}}{5}

\frac{\sqrt{5}}{5}

9000031205

Level:

Find the complex conjugate of

z = i^{5} - 3 i^{10}

3 - i

- 3 - i

- 3 + i

3 + i

9000031104

Level:

Solve the following system of equations and identify a correct statement.

\begin{aligned} \frac{x}{y + 1} - \frac{2}{x + 1} & = 0 \\ \frac{y}{x} + \frac{2}{x} & = - 1 \end{aligned}

The system has a unique solution.

The system does not have any solution.

The system has two solutions.

The system has infinitely many solutions.

9000031105

Level:

Solve the following system of equations and identify a correct statement.

\begin{aligned} \frac{1}{x + 1} - \frac{1}{y} = 0 \\ y^{2} = 1 \end{aligned}

The system has two solutions.

The system does not have any solution.

The system has a unique solution.

The system has infinitely many solutions.

9000031201

Level:

Given complex numbers

z_{1} = 1 - 2 i

and

z_{2} = 3 + 5 i

, find

z_{1} z_{2}

13 - i

13 + i

- 7 - i

13 + 11 i

9000031206

Level:

Find the opposite number to the complex number

z = \frac{1 + i}{1 - i}

- i

1

- 1

i

9000031203

Level:

Find the real part of the complex number

z = \frac{2 - i}{2 + i}

0.6

0.8

- 0.8

1

A

9000032011

9000032114

9000031202

9000031204

9000031205

9000031104

9000031105

9000031201

9000031206

9000031203

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