Roots of complex numbers and roots of unity Quiz

1. How many distinct roots does $z^5=-32$ have?

• A. $1$
• B. $5$
• C. $10$
• D. $32$

2. What is the modulus of every root of $z^4=81\mathrm{e}^{\mathrm{i}\pi/3}$?

• A. $81$
• B. $\frac{81}{4}$
• C. $9$
• D. $3$

3. The fourth root of $16\mathrm{e}^{\mathrm{i}\pi}$ with the smallest non-negative argument is

• A. $2\mathrm{e}^{\mathrm{i}\pi/4}$
• B. $4\mathrm{e}^{\mathrm{i}\pi/4}$
• C. $2\mathrm{e}^{\mathrm{i}\pi}$
• D. $2\mathrm{e}^{\mathrm{i}\pi/2}$

4. The sum of the fifth roots of unity is

• A. $1$
• B. $5$
• C. $-1$
• D. $0$

5. The sixth roots of $-1$ form a regular hexagon. Its centre and circumradius are

• A. origin, $6$
• B. $1$, $1$
• C. origin, $1$
• D. origin, $\frac16$