A complex number is any number that can be written in the form a + bi where a and b are real numbers. a is called the real part, b is called the imaginary part, and i is called the imaginary unit.
Because the square of a real number is never negative, there is no real number x such that x^{2} = -1. Mathematicians wanted this equation to have a solution.
Therefore, they defined i to be the solution of the equation x^{2} = -1 and called i imaginary number or imaginary unit. By doing this, they invented a new system of numbers called complex numbers.
What they basically did is this.
Now we use complex numbers in electromagnetism, signal processing, and many others!
Consider again the complex number a + bi. If a is not equal to 0 and b = 0, the complex number a + 0i = a and a is a real number. Therefore, all real numbers are also complex numbers.
If b is not equal to zero and a is any real number, the complex number a + bi is called imaginary number.
In other words, if the imaginary unit i is in it, we can just call it imaginary number.
If the imaginary unit i is in t, but the real real part is not in it such as 9i and -12i, we call the complex number pure imaginary number.
Here is a diagram that shows the difference between a complex number, a real number, an imaginary number, and a pure imaginary number.
Nov 21, 19 02:38 PM
What is a probability line ? Things that you must know before doing problems ...
Basic math formulas
Algebra word problems
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.