we get![\left[\begin{array}{cc}x &y\\-y&x\end{array}\right] + \left[\begin{array}{cc}\tilde{x}&\tilde{y}\\ -\tilde{y}&\tilde{x}\end{array}\right] = \left[\begin{array}{cc}x + \tilde{x}& y + \tilde{y}\\-(y+\tilde{y})&x+\tilde{x}\end{array}\right]](/tpl/images/0101/4217/ea42b.png)
.
![\left[\begin{array}{cc}x&y\\-y&x\end{array}\right]\left[\begin{array}{cc}\tilde{x}&\tilde{y}\\-\tilde{y}&\tilde{x}\end{array}\right] = \left[\begin{array}{cc}x\tilde{x}-y\tilde{y}&x\tilde{y}+y\tilde{x}\\-y\tilde{x}-x\tilde{y}&x\tilde{x}-y\tilde{y}\end{array}\right]](/tpl/images/0101/4217/f775a.png)
. 
which in terms of matrices is equivalent to find the matrix![\left[\begin{array}{cc}x&y\\-y & x\end{array}\right]^{-1}= \dfrac{1}{x^{2}+y^{2}} \left[\begin{array}{ccc}x&-y\\y&x\end{array}\right]](/tpl/images/0101/4217/3b877.png)
  
(x y
Mathematics, 17.07.2019 20:30 sammuelanderson1371
Acomplex number, represented by z = x + iy, may also be visualized as a 2 by 2 matrix
(x y
-y x)
(a) verify that addition and multiplication of complex numbers de ned via matrix opera-
tions are consistent with the usual addition and multiplication rules.
(b) what is the matrix representation corresponding to (x + iy)^-1?
Answers: 1
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Acomplex number, represented by z = x + iy, may also be visualized as a 2 by 2 matrix
(x y
(x y
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