Complex Numbers

Complex Numbers have a real component and an imaginary component. In the real number system it is not possible to take the square root of a negative number. For example, it is not possible to simplify -9 because there is not a number that when squared will equal -9. However, in the set of complex numbers it is possible to take the square root of a negative number by defining -1 as i an imaginary number.

For Example

  • -16 can be written as 16x-1 = 4i where 4 is the real number and i can represent -1

    Therefore -16 = 4i


  • -25 can be written as 25x-1 = 5i where 5 is the real number and i can represent -1

    Therefore -25 = 5i


  • -5 can be written as 5x-1 where 5 is a real number and i can represent -1

    Therefore -5 = i5


The Complex Numbers are written in the form of a + bi where a and b are real numbers and i is an imaginary number.

For Example

  • 3 + 4i Where a is 3 and b is 4 and i is the imaginary number -1.


  • 2i Can be rewritten as 0 + 2i where a is 0 and b is 2 and i is the imaginary number -1.


The key to the Complex Numbers is the understanding that i is an imaginary number that is defined as -1 and that the accepted form is a + bi where a and b are real numbers and i is the imaginary component.

Related Links:
Math
algebra
Adding Complex Numbers
Complex Numbers
Operations With Complex Numbers
Rationalizing Imaginary Denominators

Identifying Real and Imaginary Numbers Quiz
Adding Complex Numbers Quiz
Subtracting Complex Numbers Quiz
Multiplying Complex Numbers. Quiz
Dividing Complex Numbers Quiz
Mixed Complex Number. Quiz


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