Algebra, Relations and Functions — Introduction in Complex Numbers

About this lesson

This unit introduces complex numbers, beginning with the need for a new number system to solve equations like x² = -1, which have no real solutions. It defines the imaginary unit i where i² = -1, explains integer powers of i, and introduces the general form of a complex number a + bi, distinguishing real and imaginary parts. The unit covers equality of complex numbers, operations (addition, subtraction, multiplication, and division) on complex numbers, and the concept of conjugate numbers, including their sum and product. It also includes solving quadratic equations that yield complex solutions and a real-world application to electric current in parallel resistances. By the end, students should be able to simplify powers of i, perform arithmetic with complex numbers, find conjugates, solve equations involving complex numbers, and apply these skills to simple problems.