Test 24
1.
\(z=\samefrac8{1+\sqrt3i}\)
Which of the following is one of the square roots of the complex number above?
A) \(-1-\sqrt3i\)B) \(-1+\sqrt3i\)C) \(\sqrt3-i\)D) \(2\sqrt3i\)E) \(-1+3i\)
2.
\(z=4(\cos72^\circ+i\sin72^\circ)\)
Which of the following is one of the square roots of \(\overline z\)?
A) \(2\operatorname{cis}36^\circ\)B) \(2\operatorname{cis}72^\circ\)C) \(2\operatorname{cis}144^\circ\)D) \(4\operatorname{cis}324^\circ\)E) \(4\operatorname{cis}162^\circ\)
3.
\(z=27(\cos120^\circ+i\sin120^\circ)\)
Which of the following is one of the cube roots of the complex number?
A) \(27\operatorname{cis}40^\circ\)B) \(27\operatorname{cis}120^\circ\)C) \(3\operatorname{cis}160^\circ\)D) \(27\operatorname{cis}160^\circ\)E) \(3\operatorname{cis}240^\circ\)
4.
\(z=\cos120^\circ+i\sin120^\circ\)
Which of the following is one of the cube roots of the complex number?
A) \(\operatorname{cis}280^\circ\)B) \(\operatorname{cis}200^\circ\)C) \(\operatorname{cis}180^\circ\)D) \(\operatorname{cis}100^\circ\)E) \(\operatorname{cis}50^\circ\)
5.
\(z=1-i\)
Which of the following is one of the cube roots of \(\overline z\)?
A) \(\sqrt[3]{2}\operatorname{cis}\samefrac\pi4\)B) \(\sqrt[6]{2}\operatorname{cis}\samefrac{3\pi}4\)C) \(\sqrt[6]{2}\operatorname{cis}\samefrac{2\pi}3\)D) \(\sqrt[3]{2}\operatorname{cis}\samefrac{3\pi}4\)E) \(\sqrt[6]{2}\operatorname{cis}\samefrac\pi4\)
6.
\(z=\cos\samefrac\pi3-i\sin\samefrac\pi3\)
Which of the following is one of the cube roots of the complex number?
A) \(\operatorname{cis}\samefrac{4\pi}3\)B) \(\operatorname{cis}\samefrac\pi9\)C) \(\operatorname{cis}\samefrac{11\pi}9\)D) \(\operatorname{cis}\samefrac{5\pi}3\)E) \(\operatorname{cis}\samefrac\pi3\)
7.
\(z=3-4i\)
Which of the following is one of the square roots of the complex number?
A) \(1+i\)B) \(2-i\)C) \(2+i\)D) \(-1+i\)E) \(-1+2i\)
8.
\(z^2=5+8i\)
What is the ratio of the roots of the equation?
A) \(-1\)B) \(-\samefrac12\)C) \(\samefrac{1+i}{2}\)D) \(\samefrac i2\)E) \(2\)