Question

If z = x + iy, find the following in rectangular form:

`"Re"(1/z)`

Answer 1

`"Re"(1/z) = 1/(x + "i"y) xx (x - "i"y)/(x - "i"y)`

= `(x - "i"y)/(x^2 + y^2)`

= `x/(x^2 + y^2) - ("i"y)/(x^2 + y^2)`

∴ `"Re"(1/z) = x/(x^2 + y^2)`