Complex Variables and Partial Differential Equations (3130005)

BE | Semester-3   Winter-2019 | 26-11-2019

Q3) (a)

Evaluate Cx-y+i x2 dz ; Where C is a straight line from z = 0  to z = 1 + i .

The equation of straight line from 0=(0,0) to 1+i=(1,1) is
 
xy1111001 = 0
 
⟹x(1-0)-y(1-0)+1(0+0)=0⟹x-y=0⟹y=x⟹dy=dx
 
dz=dx+i dy⟹dz=dx+idx⟹dz=(1+i ) dx
 
x:0 to 1
 
I = Cx-y+i x2 dz
 
I = 01 x-x+i x2 1+i dx
 
I = i 1+i01 x2  dx = i - 1 x3301 =  i - 13