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.

Which of the following is NOT a subset of the real number system?

• Natural numbers

• Rational numbers

• Integers

• Imaginary numbers

What is the standard form of a complex number?

• a + bi

• a - bi

• a / bi

• a * bi

How would you express the real number -9 as a complex number?

• 0 + 9i

• -9 + 0i

• -9i + 0

• 0 - 9i

If a complex number is written as 2/5 + 3/5i, what are the values of a and b?

• a = 2, b = 3

• a = 2/5, b = 3/5

• a = 3/5, b = 2/5

• a = 3, b = 2

Can a and b in a complex number belong to different number systems?

• Yes, a can be a rational number and b can be a natural number

• Yes, a can be an integer and b can be an irrational number

• No, they must belong to the same number system

• No, a and b must both be real numbers