Imaginary Number's - 'i'

Classification of numbers:

• Numbers came into existence because of the need of counts. 
• We encounter the numbers or use them in our day to day lives.  
• Numbers are broadly classified into real numbers and imaginary numbers. 
• We commonly use the real numbers in our day to day life whereas we are not much familiar with the imaginary numbers.
• But imaginary numbers also have an integral part to play with, when it comes to quadratic equations, technology, electricity, etc.,

Significance of 'i':

• Imaginary numbers are usually represented by 'i'
• Imaginary numbers are NOT imaginary. They exists and has it's own applications.
• Euler gave the symbol 'i' for roots of negative numbers.
• When we take the roots of negative numbers, we get an error reply.  So to get the result of negative roots, the real numbers are multiplied by 'i' = √-1 
• Where 'i' is the 90 degree rotation to the real number axis.

Since 'i' has the property of oscillatory behavior, where it comes to its initial state after every fourth rotation, it is used in mathematically dealing with oscillating objects of circular motion.

Even though we use imaginary numbers to solve problems we will get real solutions only.

Imaginary numbers are physically not measurable. For example, in quantum mechanics while finding out the position or momentum of a particle, we get the real values and in probabilistic nature we square the wave functions in which 'i' vanishes.

Some facts about 'i':

• '0' is considered both as a real and an imaginary number.
• The vertical axis of cartesian graph is the imaginary part and the horizontal axis is the complex part,
• It is used in transmitting radio waves, cellular and wireless technologies, radar and even in brain waves, represent physical quantities such as impedence of RL, RC or RLC circuits in engineering and physics.