Problems

01

Complex arithmetic

Write each of these expressions in the form $a+bi$.

(a) $(1+3i)(5-i)$ $$ (b) ${\displaystyle \frac{2+5i}{-3+7i}}$

02

Complex solutions of quadratic equations

Find all solutions and write them in the form $z=a+bi$.

$$2z^2+z+1=0$$

03

Complex arithmetic

Write each of these expressions in the form $a+bi$.

(a) ${(2i)}^3$ $$ (b) $\sqrt{-4}\sqrt{-16}$

04

Complex solutions of quadratic equations

Find all solutions and write them in the form $z=a+bi$.

(a) $16x^2+9=0$ $$ (b) $x^2+\frac{1}{3}x+\frac{1}{9}=0$