5. Show that exp(z²) s exp(2|") for all z e C. Show that Log[(-1+i)']#2Log(-1+i). 7. Find all roots of the equation log(z) = ai / 2 %3D 6.
5. Show that exp(z²) s exp(2|") for all z e C. Show that Log[(-1+i)']#2Log(-1+i). 7. Find all roots of the equation log(z) = ai / 2 %3D 6.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let
y and v(x, y) = x' – 3xy² . Sho
functions but that their product uv is not harmonic.
4.
Show that u(x, y) = 2x-x+3xy is harmonic and f
v(x, y).
5.
Show that exp(z) s exp(z|") for all ze C.
6.
Show that Log[(-1+i)*]#2Log(-1+i).
7.
Find all roots of the equation log(z) = ri / 2
8.
Find the principal value of (1+ i)'.
9.
Use the definitions of sin(z) and cos(z) given in Lect
IT
= cos(z) for all ze C.
prove that sin z+-
(Do not use any other trigonometry identities for que
Evaluate [(3t – i)² dt
10.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcfc5bdab-6654-444e-b9d5-5fc4b8470fbb%2Fa998f341-5910-4d3d-ae74-c4bdd7e7f732%2Ffk6qws_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let
y and v(x, y) = x' – 3xy² . Sho
functions but that their product uv is not harmonic.
4.
Show that u(x, y) = 2x-x+3xy is harmonic and f
v(x, y).
5.
Show that exp(z) s exp(z|") for all ze C.
6.
Show that Log[(-1+i)*]#2Log(-1+i).
7.
Find all roots of the equation log(z) = ri / 2
8.
Find the principal value of (1+ i)'.
9.
Use the definitions of sin(z) and cos(z) given in Lect
IT
= cos(z) for all ze C.
prove that sin z+-
(Do not use any other trigonometry identities for que
Evaluate [(3t – i)² dt
10.
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