Today is the 3rd formal online class on AOPS Algebra 1 course. In today’s class, students studied the complex numbers and the operation of complex numbers, such as addition/subtraction, multiplication and division. In addition and subtraction, we only need to add/subtract real parts together and imaginary parts together. In division, it is very similar to the rationalization of denominators discussed in previous class, that is, multiplying the conjugate complex number to generate the real numbers. The concept of complex number will be used in solving quadratic equations by the completing the square. Regarding the completing the square, students need to understand how to create the perfect square by using the formula a^2+2ab+b^2=(a+b)^2. Based on this foundation, we are able to extend the knowledge into the method of solving quadratic equation, to be taught in next class.
Here is the homework assignment:
P.362, 12.2.1, 12.2.2, 12.2.3, 12.2.5
P.368, 12.3.1, 12.3.2, 12.3.3, 12.3.4
P.378, 13.1.1, 13.1.2, 13.1.3