Complex Functions for Engineering Mathematics
In Mathematics, most students will feel difficulty to grasp complex functions. Complex functions are actually a simple idea, But only thing is we have to learn it in a correct way. So here, I am giving you some ideas of complex functions including ,
- Complex Functions
- Limit of a function
- Continuity
- Differentiation function of a complex variable
- Mainly Complex Functions are those whose values are complex numbers.
- Complex variables are defined z=x+iy in which x and y are real variables.
i is an imaginary root.(i^2= -1)
- Let a second complex variable w=u+iv ,where u and v are real variables.
- If there exist a relationship between w and z, So that for each value of z in a given region of x-plane there is assigned one value of w. Then we can say that w is said to be a function of z.
= u(x,y) + i v(x,y)
x,y is real numbers and u(x,y),v(x,y) are real valued functions
- So a Complex function is a function whose domain and range are subsets of the complex plane.
- Graph of this complex functions are given below
- Domain of a function is the set of input value for which functions is defined.
- Range is normally the set of output function.
- Example:
Consider w= z^2 + z ,defined for all values of z.
We know that z=x+iy
So, w = u+iv = (x+iy) ^2 + (x+iy)
= x^2 -y^2+2ixy+x+iy
= x^2 -y^2 +x+i(2xy+y)
When we equating real and imaginary part,
we will get u= x^2 +x -y^2 and v= 2xy+y
