Test 28
1.
\(\operatorname{Arg}(z_1z_2)=\samefrac{2\pi}3\)
\(\operatorname{Arg}(\samefrac{z_1}{z_2})=\samefrac\pi6\)
\(\Rightarrow\operatorname{Arg}(z_1)=?\)
A) \(\samefrac\pi4\)B) \(\samefrac{3\pi}5\)C) \(\samefrac{5\pi}{12}\)D) \(\samefrac{3\pi}8\)E) \(\samefrac{2\pi}7\)
2.
\(z=2+i\)
\(\Rightarrow\left(\samefrac{z+\overline z}{z-\overline z}\right)^4=?\)
A) \(-16\)B) \(-16i\)C) \(16i\)D) \(16\)E) \(1\)
3.
\(1+i+i^2+i^3+\cdots+i^{78}=?\)
A) \(-i\)B) \(-1\)C) \(0\)D) \(1\)E) \(i\)
4.
\((\sqrt z+i)^3+1=|z|\)
\(\Rightarrow z=?\)
A) \(1+i\)B) \(1-i\)C) \(2-4i\)D) \(3-i\)E) \(8-6i\)
5.
\(z=-2-2\sqrt3i\)
Which of the following is one of the square roots of the complex number?
A) \(-1+\sqrt3i\)B) \(1+\sqrt3i\)C) \(\sqrt3-i\)D) \(\sqrt2(1-i)\)E) \(\sqrt2(1+i)\)
6.
\(|z-6i|\le6\)
Which graph represents the solution set?
A) B) C) D) E)
7.
\(z=\sin50^\circ+(1+\cos50^\circ)i\)
\(\Rightarrow\operatorname{Arg}(z)=?\)
A) \(25^\circ\)B) \(40^\circ\)C) \(65^\circ\)D) \(70^\circ\)E) \(85^\circ\)