Complex conjugates and polynomial roots Quiz

1. A polynomial has real coefficients and a root $3-2i$. Which must also be a root?

• A. $-3+2i$
• B. $-3-2i$
• C. $3+2i$
• D. $2-3i$

2. A real quartic has roots $1+i$ and $2-3i$. Which other two roots must it have?

• A. $1-i$ only
• B. $1-i$ and $2+3i$
• C. $-1-i$ and $-2+3i$
• D. $2+3i$ only

3. Which real quadratic has roots $3\pm i$?

• A. $z^2+6z+10$
• B. $z^2-6z+8$
• C. $z^2-6z-10$
• D. $z^2-6z+10$

4. A real cubic has roots $2$ and $i$. What is the third root?

• A. $-i$
• B. $-2$
• C. $2i$
• D. $1$

5. Solve $z^2-2z+5=0$.

• A. $1\pm i$
• B. $1\pm2i$
• C. $-1\pm2i$
• D. $2\pm4i$