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Complex Numbers

There are situations in which Real Numbers are not enough, for example when we solve a quadratic equation and we find the square root of a negative number.
To solve these problems, we define the imaginary unit or unit imaginary number “i” as a number such that

Now we can solve negative square roots:

Or solve all the quadratic equations:


Then the Complex Numbers set is:

Examples: 2-7i, 3+πi, -20i, 157’28-i, 1428


  a + bi is called binomial form of a complex number. a is called real part and b imaginary part.


  Now, we have these sets of numbers:


  We can represent the Complex Numbers in the plane:



True or false

Decide if the following sentences are true or false:

Pregunta 1

a) All the Rational Numbers are Complex Numbers

Pregunta 2

b) All the Real Numbers are Natural Numbers

Pregunta 3

c) All the Irrational Numbers are Complex Numbers

Pregunta 4

d) e and i are Real Numbers