Numbers and Imaginary numbers

Numbers and imaginary numbers are important components of complex numbers in mathematics.

     

 1. Real Number

 

  ✔ Definition:

  Real numbers are all numbers that can be expressed on a number line.

   

 ✔ Types of real numbers:

  Integers (e.g. -2, 0, 3)

  Rational numbers (e.g. 1/2, -3/4, 2)

  Irrational numbers (e.g. √2, π)

 

 ✔ Examples:

 3, 0, -1.5, √2, π

 Real numbers are the numbers we mainly use in our daily lives.

 

2. Imaginary Number

 

✔ Definition:

 Imaginary numbers are numbers that become negative when squared. In real numbers, any number squared is either positive or 0, but imaginary numbers are a concept that extends that rule.

 

✔ Imaginary Unit  i :

Imaginary is defined based on the imaginary unit  i  as follows:

 i=√(-1)

 Therefore:

  i^2=-1

 This does not exist in the real domain, but it is established in the extended complex system.

 

 ✔ Examples of imaginary numbers:

  2i, -i, \sqrt{3}i 

 

 3. Complex Number

  A complex number is a number that is made by combining a real number and an imaginary number.

 Its form is as follows:

  a+bi

  a : real part

  b : imaginary coefficient

  i : imaginary unit

 

  ✔ Examples:

    3 + 2i : real number 3, imaginary number 2i

   -1 - 4i : real number -1, imaginary number -4i

 

Why is it important? Complex numbers are important in many fields of science and engineering, including electrical engineering, physics, signal processing, and quantum mechanics.