Question

A transformation of that type w is equal to alpha multiplied into z + beta where alpha and beta complex constant is known as

Answer 1

$its \: known \: as \: bi - linear \: \: or \\ mobius \: \: transformation. \\ in \: fact \: given \: form \: is \: a \: special \\ case \: of \: it \: w = \frac{az + b}{cz + d} \\ where \: c = 0 \: \: and \: \: d = 1$

Answer 2

The transformation is known as mobius transformation.

A transformation of that type where,

w = α × (z + β)

[Where α and β are complex constant.]

This type of transformation is known as bi-linear transformation or, mobius transformation.

The given scenario is a special scenario of the following equation,

w = (az + b)/ (cz + d)

Where, c = 0 and d = 1.

From this, we can get the values of α and β.