Mathematical basis of information and communication -- the first experiment

The first part

1,(1)
For complex numbers without variables, use Re,Im,Abs,Arg You can work out

1,(2) For complex numbers with variables, we need to define the range of variables as real numbers , Then you can use the previous commands normally （ here Abs Instead of Norm）

1,(3)

1,(4)

2, The first 2 In the same way, the scope should be specified first , However, the result of direct calculation is not simplified , Here, you can use spanning to simplify the operation

3, Use Sovle Solve the equation by /. Convert the result into a sequence and draw the set of points in the sequence
（1）

（2）

（3）

（4）

（5） Here is an infinite point , So here we use a loop to complete an approximation

4,（1） Draw area RegionPlot



(2)

The first 2 part
1, Differential use Dt
（1）

（2）

2,
First find the real part function, then find the imaginary part function , According to Cauchy - Riemann equation solves the differentiable region

The solution is a point , So at this point we can derive , But all regions are not resolvable
3, Solve the complex equation , You can use reduction to make the result look better
（1）

（2）

（3）

4, Corsey - Riemann solves the equation

5, Find integral , Two ways 1, It is best to use parametric equations for complex integrals , The way 2, Use residue to get integral
（1）

（2） Parametric equation solving integral

6, Find the derivative of the implicit function , Simply double the differential , The use of Jacobian determinant to derive multivariate and multigroup
（1）

（2）u2x Express u Yes x Partial derivative of , The rest is the same