Roots of complex numbers Quiz

1. How many different roots has $z^6=-1$?

• A. $3$
• B. $12$
• C. $1$
• D. $6$

2. The roots of $z^4=16$ are

• A. $2,\,2i,\,-2,\,-2i$
• B. $4,\,4i,\,-4,\,-4i$
• C. $2,\,-2$ only
• D. $2e^{i\pi/4}$ and its conjugates

3. The principal argument of $-1-i$ is

• A. $\frac{3\pi}{4}$
• B. $-\frac\pi4$
• C. $-\frac{3\pi}{4}$
• D. $\frac\pi4$

4. One cube root of $-8$ is

• A. $2$
• B. $2e^{i\pi/3}$
• C. $2e^{i\pi/2}$
• D. $\sqrt[3]{8}i$

5. The sum of the five fifth roots of $1$ is

• A. $5$
• B. $0$
• C. $1$
• D. $-1$