Question

# Let z=x+iy be a complex variable. Consider that contour integration is performed along the unit circle in anticlockwise direction. Which one of the following statements is NOT TRUE?

A
The residue of zz21 at z=1 is 1/2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Cz2dz=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
12πiC1zdz=1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
¯¯¯z (complex conjugate of z) is an analytical function
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct option is D ¯¯¯z (complex conjugate of z) is an analytical functionWe will go through options (a) f(z)=zz2−1 Resf(z)=limz→1(z−1)f(z)=limz→11z+1=12 (b) f(z)=z2 is analytic every where By cauchy's theorem ∮Cz2dz=0 (c) By Cauchy integral formula 12πi∮Cf(z)dzz−z0=f(zo) ⇒12πi∮C(1z−0)dz=f(0)=1 (d) f(z)=¯¯¯z=x−iy u=x,v=−y ux=1,vx=0 y=0,vy=−1 ux≠vy f(z) does nto satisfy C.R equ ⇒f(z) is not analytic

Suggest Corrections
0