Test 23
1.
\(i^2=-1\)
\(z=-9\)
Which of the following are the square roots of the complex number above?
A) \(\{-i,i\}\)B) \(\{1-i,1+i\}\)C) \(\{3i,-3i\}\)D) \(\{\sqrt3i,-i\}\)E) \(\{1,-1\}\)
2.
\(z=9(\cos300^\circ+i\sin300^\circ)\)
Which of the following is one of the square roots of the complex number above?
A) \(\samefrac{-\sqrt3+i}{2}\)B) \(\sqrt3-i\)C) \(-3\sqrt3+3i\)D) \(-\samefrac{3\sqrt3}{2}+\samefrac32i\)E) \(-\samefrac13+\samefrac{\sqrt3}{3}i\)
3.
\(z=\sqrt3+i\)
Which of the following is one of the square roots of the complex number above?
A) \(\sqrt2\operatorname{cis}15^\circ\)B) \(2\operatorname{cis}30^\circ\)C) \(\sqrt2\operatorname{cis}75^\circ\)D) \(\operatorname{cis}195^\circ\)E) \(2\operatorname{cis}185^\circ\)
4.
\(z=4i\)
Which of the following is one of the square roots of the complex number above?
A) \(2-2i\)B) \(1-i\)C) \(1+i\)D) \(2+i\)E) \(\sqrt2+\sqrt2i\)
5.
\(z=-2+2\sqrt3i\)
Which of the following is one of the square roots of the complex number above?
A) \(1-i\)B) \(1+\sqrt3i\)C) \(1-\sqrt3i\)D) \(-1+\sqrt3i\)E) \(2+2i\)
6.
Which of the following is one of the square roots of z?
A) \(3+3\sqrt3i\)B) \(1+\sqrt3i\)C) \(1-\sqrt3i\)D) \(\samefrac{3\sqrt3}{2}+\samefrac32i\)E) \(\samefrac32+\samefrac{3\sqrt3}{2}i\)
7.
\(z^2=4i\)
Which of the following could be one of the roots?
A) \(-\sqrt2-\sqrt2i\)B) \(\sqrt2-\sqrt2i\)C) \(-\sqrt2i\)D) \(\sqrt3-\sqrt3i\)E) \(\sqrt3-2i\)
8.
\(z=\samefrac{\sqrt3+3i}{\sqrt3}\)
What are the square roots of z?
A) \(\{\sqrt2\operatorname{cis}15^\circ,\sqrt2\operatorname{cis}195^\circ\}\)B) \(\{2\operatorname{cis}30^\circ,2\operatorname{cis}210^\circ\}\)C) \(\{\sqrt2\operatorname{cis}60^\circ,\sqrt2\operatorname{cis}240^\circ\}\)D) \(\{\sqrt2\operatorname{cis}30^\circ,\sqrt2\operatorname{cis}210^\circ\}\)E) \(\{2\operatorname{cis}30^\circ,2\operatorname{cis}240^\circ\}\)