Question

What is the difference between real and imaginary roots?

Answer 1

Hint: In this we need to explain the difference between the real and the imaginary roots. Mathematically, complex numbers are represented as \[x\ + \ iy\] where \[x\] and \[y\] are the real numbers and here \[i\] is an imaginary number. The set of complex numbers is basically denoted by \[C\] . Usually, complex numbers consist of two parts namely real parts and imaginary parts . Here we need to spot the difference between the real roots and the imaginary roots.

Complete answer:
Real roots are expressed as the real numbers. Real numbers can be positive as well as negative including zero. Real numbers include all the rational numbers and the irrational numbers.
There are other types of numbers which aren’t on the number line that are known as complex numbers.
Complex number consists of two parts namely the real part and the imaginary part. It is the sum of real numbers and imaginary numbers. In the general form \[a\ + \ ib\] Here a is the real part and ib is the imaginary part . Imaginary part is denoted by Im(z) and the real part is denoted by Re(z).
Mathematically, imaginary numbers are multiples of something called an imaginary unit which can be written in the letter of \[i\] . And this imaginary unit has an unusual property that is the value of the square of the imaginary unit is equal to minus of \[1\] which property is not in real numbers.
The imaginary roots are used in formulas and equations whereas real numbers are used in basic arithmetic.
Let us consider a complex numbers,
\[4i\] , it can be written as \[0\ + \ 4i\] which is in the form of \[a\ + \ ib\] . Here real part is \[0\] and the imaginary part is \[4i\] which is non zero hence such numbers are known as purely complex numbers
Final answer :
Real roots are expressed using only real numbers while expressing imaginary roots are expressed using imaginary numbers.

Note:
Mathematically, every real number can be written in the form of a complex number, hence every real number is a complex number. The value of the imaginary number \[i^{2}\] equals the minus of \[1\] . The value of the unit imaginary number \[i\] equals the square root of minus \[1\] . And the imaginary number \[i\] leads to another topic that is the complex plane . Example for complex numbers is \[(2 + 3i)\] .