Question For a linear transformation w = (a + jb)z, the

Grady Turner

Grady Turner

Answered question

2021-11-30

Question
For a linear transformation w=(a+jb)z, the point A=(1+j) in the z-plane was transformed to A=(5+14j) in the w-plane. Calculate (a+jb), the magnification, and the rotation of the transformation.

Answer & Explanation

Rex Gibbons

Rex Gibbons

Beginner2021-12-01Added 6 answers

Step 1
Rotalion and magnition: - A transformation of the form ω=αz,αi complex no.
and if α=λeiθ, then λ is magnition whine θ is Rotalion.
Now
w=(a+jb)z then w=5+14j
so from
5+14j=(a+jb)(1+j)
5+14j=(ab)+j(a+b)
ab=5
a+b=14
Solving
a=92
b=192
Hence
ω=(92+j192)z
put 92=λcos,192=λsinθ
λ=2212
tan=199
θ=tan1(199)
w=2212e{tan1(199)}z
Now
(1) a+j3=92+j192
(2) magnition=2212
(3) Rotelion=tan1(199)

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