Manipulating Complex Numbers to Simplify Expressions and to Solve Equations.

How should I imagine an imaginary number? What is a complex number? Why all real numbers are complex numbers, but not all complex numbers are real numbers? What is that little "i"? ... How do I start the solution of an equation that has imaginary numbers? What is the difference between the imaginary part and the real part of a complex number?

This lesson takes a great deal of care in simplifying the presentation of these concepts. You will have the opportunity to view several types of expressions that contain complex numbers. After this lesson, you won't be afraid to tackle complex numbers in expressions and equations!

Lesson's Content

Lesson's Glossary

Complex Number: Number of the form a + bi, where the real part is a and the imaginary part is bi; both a and b are real numbers and i is the square root of -1.

Complex number plane: A plane with perpendicular number lines, where the horizontal is the real part of a complex number and the vertical one is the imaginary part.

Conjugates: Binomials in the form a√b +c√d and  a√b -c√d for which a, b, c, and d are rational numbers.

i It is the imaginary unit. The one to indicate the imaginary part of a complex number. i is the square root of -1.

Imaginary Number: A number in the form of bi, where i2 = -1 and thus i is the square root of -1.

Real number:  Any number rational or irrational, with exception of the imaginary numbers all numbers are real numbers.

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