Compute u and v (z=x+iy, w=u+iv) if w=(2z-1)/(2-z). Determine the image of the unit circle by this transformation.

Scott Valenzuela

Scott Valenzuela

Answered question

2022-11-29

Compute u and z = x + i y, w = u + i v) if w = 2 z 1 2 z . Determine the image of the unit circle by this transformation.

Answer & Explanation

Melanie Wong

Melanie Wong

Beginner2022-11-30Added 11 answers

From where you left off,
| 2 w + 1 | = | 2 + w |
Now write
w = u + i v
and simplify the expression by writing down the modulus and squaring both sides. You end up with
u 2 + v 2 = 1
which is also the unit circle in the w−plane

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