Find modulus, argument of 1/z + 1/(2 - 1/z + 1) for z = 3-2i

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Apr 6, 2007
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Hello, is this problem:

Find the modulus and argument of 1/z+1/(2-1/z+1), when z=3-2i.

Is it just asking me to put 3-2i in everywhere I see z?
 
Ruby said:
Is it just asking me to put 3-2i in everywhere I see z?
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It is asking you to find the modulus and argument of the expression, after having plugged "3 - 2i" in for "z".

What do you get when you simplify the expression?

What are the definitions of "modulus" and "argument"?

Please be specific. Thank you.

Eliz.
 
Okay, so the modulus is the absolute value, and the argument is the amplitude. I wrote the equation out with the 3-2i and I have no idea how to start simplifying it.
 
Is this the exact expression: \(\displaystyle \L \frac{1}{z} + \frac{1}{{2 - \frac{1}{{z + 1}}}}?\)

If not please correct your posting. Because these are complex variables we must end up with a very simple expression in the form of A+Bi. Now yes, one way to do that is to simply substitute 3-2i for z. BUT then you have a lot of messy algebra to do to reduce it to the A+Bi format. Reply with what you did.
 
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