Introduction to the Complex Number System

This lesson introduces the complex number system by extending the real number system. It reviews various number systems, including natural, integer, rational, and irrational numbers, which together form the real number system. The lesson explains imaginary numbers and the imaginary unit 'i', which is the square root of negative one. It demonstrates how to form complex numbers by combining real and imaginary parts, using examples like 6 + 3i. The lesson also covers writing real and imaginary numbers in complex form, such as -9 as -9 + 0i and -2i as 0 - 2i. It explores complex numbers with components from different number systems, like -8 + √55i. Finally, it summarizes the complex number system, which includes real and imaginary numbers, forming complex numbers like 2 + 5i.

Can a and b in a complex number belong to different number systems? Provide an example.

What types of numbers are included in the complex number system?