9000035706 Level: AFind the absolute value of the complex number \(z = \frac{2+6\mathrm{i}} {1-2\mathrm{i}}\).\(2\sqrt{2}\)\(2\sqrt{5}\)\(2\)\(2\sqrt{3}\)
9000035708 Level: AFind the imaginary part of the complex number \(z=1 + 2\mathrm{i}^{12} + 3\mathrm{i}^{19} -\mathrm{i}^{22} + 2\mathrm{i}^{105}\).\(- 1\)\(- 5\)\(1\)\(4\)
9000035707 Level: AFind the real part of the complex number \(z= 2 + 2\mathrm{i}^{2} + \mathrm{i}^{3} -\mathrm{i}^{4} + 2\mathrm{i}^{5}\).\(- 1\)\(1\)\(5\)\(- 3\)
9000035802 Level: CSolve the following equation for \(z\in \mathbb{C}\). By \(\overline{z }\) the complex conjugate of \(z \) is denoted. \[ 3z - 2\overline{z } = 8 - 10\mathrm{i} \]\(8 - 2\mathrm{i}\)\(1 + 5\mathrm{i}\)\(8 - 10\mathrm{i}\)\(2 + 2\mathrm{i}\)
9000035701 Level: AWhat is the algebraic form of the complex number \( A \) graphed in the complex plane (as shown in the picture)?\( -3 + 2\mathrm{i}\)\( 2 - 3\mathrm{i}\)\( 2 + 3\mathrm{i}\)\( -3 - 2\mathrm{i}\)
9000034803 Level: AFind the complex conjugate of \(z = 1 - 3\mathrm{i}\).\(1 + 3\mathrm{i}\)\(- 1 - 3\mathrm{i}\)\(- 1 + 3\mathrm{i}\)\(1 - 3\mathrm{i}\)
9000034802 Level: AFind the opposite number to the complex number \(z = 3 -\mathrm{i}\).\(- 3 + \mathrm{i}\)\(- 3 -\mathrm{i}\)\(3 + \mathrm{i}\)\(3 -\mathrm{i}\)
9000034805 Level: AFind the complex number \(z\) which satisfies \(2z = 2 - 3\mathrm{i}\).\(1 -\frac{3} {2}\mathrm{i}\)\(- 3\mathrm{i}\)\(4 - 6\mathrm{i}\)\(- 1 + \frac{3} {2}\mathrm{i}\)
9000034807 Level: BFind the polar form of the complex number \(z = 2\mathrm{i}\).\(2\left (\cos \frac{\pi }{2} + \mathrm{i}\sin \frac{\pi }{2}\right )\)\(\sqrt{2}\left (\cos \frac{\pi }{2} + \mathrm{i}\sin \frac{\pi }{2}\right )\)\(\cos \frac{\pi }{2} + \mathrm{i}\sin \frac{\pi }{2}\)\(2\left (\cos 0 + \mathrm{i}\sin 0\right )\)