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?

Step-by-step explanation:

A) Suppose that we have the complex numbers

Remember that to sum complex numbers, we sum the real parts of the two numbers to get the real part and the imaginary parts of the two numbers to get the imaginary part. Hence,  

On the other hand, if we sum the matrix visualizations of we get

which is the matrix visualization of .

To multiply two complex numbers, we use the distributive law to multiplly and then separete the real part from the imaginary part

Again, if we multiply the matrix visualizations of we get

which is the matrix viasualization of

B)  Since the usual matrix operations are consisten with the usual addition and multiplication rules in the complex numbers, we can use them to find the multiplicative inverses of a complex number .

We are looking for the complex number which in terms of matrices is equivalent to find the matrix

Hence,

rounding to the nearest thousandth would be 452,000

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.