Do you  think that the matrices we introduced in this discussion are good  stand-ins for complex numbers? Explain your reasoning.  Is there any  operation/task where they might fail to “impersonate” complex numbers?

To me matrices are usually harder to solve than doing the work for  complex numbers. It's a different way of thinking about the numbers than  I am used to, and adds more "rules" to remember.

• If all you needed to do with complex numbers was add them, which format would you choose to use? Briefly explain.
• If all you needed to do with complex numbers was multiply them, which format would you choose to use? Briefly explain.
• If you needed to add, multiply, and find magnitudes for complex numbers which format would you choose to use? Briefly explain.

For all three questions above I would rather use rectangular form as  of right now. Complex numbers are added/multiplied the same as any other  algebra problem, as long as you keep in mind if a i2 comes  up its no longer representing an imaginary number, but -1, you can do  the math the same as if it had an x instead of an i.