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.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520​

Please share your work/thoughts about this problem.

 

[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:
\(f\left[ {\begin{array}{*{20}{c}}
a \\
b
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
1&{ 1} \\
{ - 1}&1
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
a \\
b
\end{array}} \right]\)\( = \left[ {\begin{array}{*{20}{c}}
{a + b} \\
{b - a}
\end{array}} \right]\)