As said by Jan regarding constant value $\pi$ ,Imagine you have a circle and you are able to measure its circumference "c". Then, you can also find out what its diameter "d" is. When you divide circumference by diameter, that is "c/d" you get a number. When you try this on various circles, and if you measure "c" and "d" more and more precisely, you will see that you get some constant, that is called $\pi$.
Similarly there are many other extremely important constants . So can anybody tell me how values of the constants are derived mathematically like the imaginary unit $j$, Euler value $e$, electric charge etc?
There are a whole bunch of ways to determine the values of different constants. I'll tell you about some of the historic methods.
$\pi$
One of the oldest methods used was the exhaustion method, by Archimedes. He put a circle in between two polygons of equivalent sides and gradually increased the number of sides until the two became nearly identical, leading him to determine the area of the circle.
e
The first person to approximate this was Jacob Bernoulli, who solved the limit of $$\lim_{n\to\infty}\left(1+\frac{1}{n}\right)^n$$
Later, in his Introductio in Analysin infinitorum, Euler used a power series (the MacLaurin series for $e^1$) to approximate $e$: $$e=\sum_{n=0}^{\infty}\frac{1}{n!}$$
$\gamma$
Euler first explored the Euler-Mascheroni constant by investigating another limit: $$\gamma=\lim_{n\to\infty}\left(- \ln n +\sum_{i=1}^n\frac{1}{i}\right)$$
$i$
The imaginary unit isn't really a constant; it's the basis for a whole new system of numbers. It has no real-number value. The only way you could efficiently relate it to real numbers would be to use its definition: $$i=\sqrt{-1}$$
On an interesting note, $\pi$, $e$ and $\gamma$ were all determined by limiting methods.