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are the following mappings transformations of the complex plane:(a). z --> 2z+1(b). x + yi --> x^2+y^2i

Question

are the following mappings transformations of the complex plane:

(a). z --> 2z+1

(b). x + yi --> x^2+y^2i

 

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Step 1

A complex transformation is a mapping on the complex plane ...

(a)
and f()=u+ iv
Let xiy
f() 2: +
ui 2(xy) +1
uiv(2x 1+ i2y
u 2x1 and v= 2y
Clearly the function u and v are real functions of two variables
is transform ed to (2x1,2y)
By definition, the map 2z1 is a complex transformation
and (x,
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(a) and f()=u+ iv Let xiy f() 2: + ui 2(xy) +1 uiv(2x 1+ i2y u 2x1 and v= 2y Clearly the function u and v are real functions of two variables is transform ed to (2x1,2y) By definition, the map 2z1 is a complex transformation and (x,

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