The line from the point 5+0i to 5+4i has length 4 units. 

The line from the point 0+1i to 3+1i has length 3 units.  

By the theorem pythagoras we know that the hypoteneuse2=sum of squares of other two sides.  (Pythagoras theorem examples)


In the diagram we can see that one of the sides =a
The other side is =b

So the side or the hypoteneuse is equal to the sum of the squares of the other 2 sides 


Therefore if we get the square root of both sides we get the modulus formula.