Complex numbers and quadratic, cubic and quartic equations Quiz

1. Calculate $(2+3i)(4-i)$.

• A. $8-3i$
• B. $11+10i$
• C. $5+10i$
• D. $8+3i$

2. Solve $z^2-4z+13=0$.

• A. $z=2\pm9i$
• B. $z=4\pm3i$
• C. $z=-2\pm3i$
• D. $z=2\pm3i$

3. A cubic with real coefficients has roots $1$ and $2-i$. What is the third root?

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

4. Write $\frac{1}{1+i}$ in the form $x+iy$.

• A. $1-i$
• B. $\frac12+\frac12i$
• C. $\frac12-\frac12i$
• D. $-\frac12-\frac12i$

5. What is the modulus of $-1+i$?

• A. $0$
• B. $2$
• C. $1$
• D. $\sqrt2$