Question

Show that the product of z = x+yi and the expression z^-1 equals 1

Answer 1

okay so
1/z = z^-1

Answer 2

(x+yi)
-----
(x+yi)

Answer 3

if you are uncomfortable with saying that is 1, multiply top and bottom by conjugate

Answer 4

(x+yi) (x-iy) x^2+y^2
-------------- = ---------- =1
(x+yi) (x-iy) x^2+y^2

Answer 5

I understand, Thank you so much! It is simpler than it looks