Determining the matrix for a transformation

[Tgl]

A transformation maps the complex number z = x + yi onto z’ such that z’ = (1-I)z.

How does one determine the matrix of this transformation?

 

[Deleted member 4993]

A transformation maps the complex number z = x + yi onto z’ such that z’ = (1-I)z.

How does one determine the matrix of this transformation?

Please show us what you have tried and exactly where you are stuck.

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[pka]

A transformation maps the complex number z = x + yi onto z’ such that z’ = (1-I)z.
How does one determine the matrix of this transformation?

Please review what you posted: $z'={\large(1-l})z$.
Did you not mean $\large z'=(1-i)z~?$

 

[pka]

To TQL; you did not answer, so we assume the mapping is $f(a+bi)=(a+bi)(1-i)=(a+b)+i(b-a)$
Here $z=a+bi$ where $\Re(z)=a~\&~\Im(z)=b$ using a two dimensional complex space we get:
\(f\left[ {\begin{array}{*{20}{c}}
a \\
b
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
1&{ 1} \\
{ - 1}&1
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
a \\
b
\end{array}} \right]\)\( = \left[ {\begin{array}{*{20}{c}}
{a + b} \\
{b - a}
\end{array}} \right]\)