Transformation z to w plane \(\displaystyle{z}^{{{2}}}-{2}+{4}={0}\)

Angelina Kaufman

Angelina Kaufman

Answered question

2022-04-08

Transformation z to w plane
z22+4=0

Answer & Explanation

veselrompoikm

veselrompoikm

Beginner2022-04-09Added 12 answers

Step 1
Try
z=2ww1+2.
It should help.
Let ww1=x
Thus,
z22z+4=(2x+2)22(2x+2)+4
=4(x2x+1).
prangijahnot

prangijahnot

Beginner2022-04-10Added 17 answers

Step 1
Michael Rozenberg's answer is better than mine, because I supplied a transformation from w to z, when the problem asked for a transformation from z to w.
z=2ww1:
this simultaneously satisfies the constraints on both terms that have a w in them.
under this transformation,
2z=4ww1
and z2=4w2(w1)2.
Therefore, the constraint that z22z+4=0 continues to be satisfied in the w plane.

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