Write f(z) in the form f(z) = u(x, y) + iv(x, y). a) f(2) = z3 b) f (z) = 4. Write f(z) in polar form f(z) = u(r,0)+ iv(r,0). f (z) = z° +4z2 –6 5. Sketch the region onto which the sector r< 2, t/ 4<0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Question 4
Write f(z) in the form f(z) = u(x, y) + iv(x, y).
a)
f(2) = z3
b)
f(z) =
4.
Write f(z) in polar form f (z) = u(r,0)+ iv(r,0).
f (z) = z° +4z2 –6
5.
Sketch the region onto which the sector r< 2, r /4<0<a/2 is mapped by the
transformation w=
6.
Find the image of the semi-infinite strip x2 0, 0< y<a under the
transformation w = e² , and label the corresponding portions of the boundaries.
7.
Use the ɛ, 8 - definition of a limit to prove the following limit.
lim (az +b) = azo + b, for complex numbers a and b with a # 0.
0z + 2
8.
Use Limit Laws to evaluate the following limits:
iz
a) lim
3
- 1
lim (z – 4z + 2+5i)
4z2
b)
c)
lim
z →i z+i
z → 2+i
z → 0 (z – 1)2
3.
Transcribed Image Text:Write f(z) in the form f(z) = u(x, y) + iv(x, y). a) f(2) = z3 b) f(z) = 4. Write f(z) in polar form f (z) = u(r,0)+ iv(r,0). f (z) = z° +4z2 –6 5. Sketch the region onto which the sector r< 2, r /4<0<a/2 is mapped by the transformation w= 6. Find the image of the semi-infinite strip x2 0, 0< y<a under the transformation w = e² , and label the corresponding portions of the boundaries. 7. Use the ɛ, 8 - definition of a limit to prove the following limit. lim (az +b) = azo + b, for complex numbers a and b with a # 0. 0z + 2 8. Use Limit Laws to evaluate the following limits: iz a) lim 3 - 1 lim (z – 4z + 2+5i) 4z2 b) c) lim z →i z+i z → 2+i z → 0 (z – 1)2 3.
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