1003082403 Level: BFind the argument of the complex number \( 2\left(\cos60^{\circ}-\mathrm{i}\cdot\sin60^{\circ}\right) \).\( 300^{\circ} \)\( 60^{\circ} \)\( 120^{\circ} \)\( 240^{\circ} \)
1003082402 Level: BFind the argument of the complex number \( 4\left(\cos\frac{\pi}3+\mathrm{i}\cdot\sin\frac{\pi}3\right) \).\( \frac{\pi}3 \)\( \frac{4\pi}3 \)\( 4 \)\( \frac{5\pi}3 \)
1003082401 Level: BFind the argument of the complex number \(\sqrt2\left(\cos160^{\circ}+\mathrm{i}\cdot\sin160^{\circ}\right) \).\( 160^{\circ} \)\( 200^{\circ} \)\( \sqrt{2} \)\( 340^{\circ} \)
1103079904 Level: AGiven the complex numbers \( u = 1 + 2\mathrm{i} \) and \( v = 2 -\mathrm{i} \), choose the diagram which shows the complex number \( z \), such that \( z = u^2 - v^2 \).
1103079903 Level: AThe diagram shows in red all the complex numbers \( z \) such that:\( |z- 1 + \mathrm{i}| = 2 \)\( |z- 1 - \mathrm{i}| = 2 \)\( |z + 1 - \mathrm{i}| = 2 \)\( |z + 1 + \mathrm{i}| = 2 \)
1103079902 Level: AThe diagram shows in red all the complex numbers \( z \) such that:\( |z + 1 + 2\mathrm{i}| < 1 \)\( |z - 1 - 2\mathrm{i}| < 1 \)\( |z + 1 - 2\mathrm{i}| < 1 \)\( |z - 1 + 2\mathrm{i}| < 1 \)
1103079901 Level: AThe diagram shows in red all the complex numbers \( z \) such that:\( |z + \mathrm{i}| \geq 2 \)\( |z - \mathrm{i}| \geq 2 \)\( |z + 1| \geq 2 \)\( |z - 1| \geq 2 \)
1103067710 Level: AAssuming \( |z - 1| \leq 2 \), choose a diagram, which shows in red all the complex numbers \( z \).
1103067709 Level: AChoose a diagram, which shows in red all the complex numbers whose absolute value is three.
1003067708 Level: ALet \( z=\frac{1-\mathrm{i}}{1+\mathrm{i}}+\frac{1+\mathrm{i}}{1-\mathrm{i}} \). If \( z \) is a complex number, find its absolute value.\( 0 \)\( 2 \)\( 4 \)Number \( z \) is not a complex number.