This activity combines the skills of solving quadratic equations having complex solutions with the skills of performing operations with square roots and complex numbers.There are given 26 quadratic equations in standard form, having rational and irrational coefficients , marked with the letters of the alphabet.
Activity Directions: Students get started with calculations of the discriminant of each of the equations to determine which of the equations have complex solutions. The aim of this first task is to confirm the knowledge that a negative discriminant indicates complex roots. Then partners solve only the equations having complex solutions.
The second task that students must complete is to sort the equations according to their complex roots into four different groups. For instance, equations which have rational real and rational imaginary parts of their roots come under one category and equations which have irrational real and irrational imaginary parts of their roots belong to another category. Partners are instructed to record the letter of each equation in its corresponding section of a “sorting mat” given. As a result there will be four different sections with letters written in them. Partners search to find only one word in each section.
Students show detailed solutions on student recording sheets specially designed for this activity or they can solve the problems on a separate sheet of notebook paper.
All answer keys are provided.