Elementary Transformation (i) Translation 𝑤= 𝑧+𝛃 .

Complex Analysis Theorem from Conformal transformation

Elementary transformation

A) Translation:

the map defined by
𝑤= 𝑧+𝛃
is called a translation in this transformation the figure in 𝑤 plane is the same as the figure in 𝑧 plane with a different origin.

Example :-

A rectangular domain 𝑹 be bounded by 𝑥=0, 𝑦=0, 𝑥=2, 𝑦=1 . Determine the region 𝑹' of 𝑤 plane into which 𝑹 is mapped under the transformation
𝑤= 𝑧+(1-2𝑖)

𝐒𝐎𝐋𝐔𝐓𝐈𝐎𝐍 :-

Given that 𝑤= 𝑧+(1-2𝑖)
𝑢+𝑖𝑣=𝑥+𝑖𝑦+(1-2𝑖)
𝑢+𝑖𝑣=(𝑥+1)+𝑖(𝑦-2)
𝑢=(𝑥+1) and 𝑣=(𝑦-2)
When 𝑥=0 then 𝑢=1
When 𝑥=2 then 𝑢=3
When 𝑦=0 then 𝑣=-2
When 𝑦=1 then 𝑣=-1
The required image is rectangular region 𝑹' bounded by 𝑢=1,𝑢=3,𝑣=-2 and 𝑣=-1 in 𝑤 plane corresponding to rectangular region
𝑹 bounded by 𝑥=0, 𝑦=0, 𝑥=2, 𝑦=1 in 𝑧 plane .
See figure in video
We can say that each point of 𝑹 is mapped into one and only one point of 𝑹' and conversely. Hence the transformation perform a translation of rectangular region. Therefore the rectangle 𝑹 is translated in the direction of the vector (1-2𝑖).
------------------------------------------------------------------
Solved...!!!
.
.
.
#complexanalysis #csirnet #conformal
#isogonal #transformation #mapping
.
🔥🔥🔥Hurry Up Students for whole detailed Videos with Answer in Description for making notes 🔥🔥🔥

🔥🔥🔥JOIN JOIN JOIN JOIN 🔥🔥🔥

🔥🔥🔥All B.Sc., B.Tech , M.Sc. , M.A. Mathematics students join with us A great platform to get knowledge in Mathematics and science... Stay tuned....for detailed videos on whole SYLLABUS with topic wise...and also join us for CSIR-UGC National Eligibility Test (NET) for Junior Research Fellowship and Lecturer-ship COMMON SYLLABUS FOR PART 'B' AND 'C' MATHEMATICAL SCIENCE 🔥🔥🔥
------------------------------------------------------------------
Channel Link: 🔥🔥🔥

Videos links 🔥🔥🔥
👇👇👇👇
------------------------------------------------------------------

----------------------------‐-------------------------------------
------------------------------------------------------------------
Play List ( Complex Analysis)

------------------------------------------------------------------
------------------------------------------------------------------
Kindly join Telegram channel 🔥🔥🔥

------------------------------------------------------------------