Question

Is there a nice result for z/z* ? (z* being the complex conjugate of z)

Answer 1

What is
\[z*z^{*}\]
\[z=a+ib\]
\[z ^{*}=a-ib\]
Then,
\[z/z ^{*}=(a+ib)/(a-ib)\]
Try to simplify the last expression?

Answer 2

So I can multiply by \[\frac{ a+bi }{ a+bi }\] to get \[z/z*=(a+bi)^2/(a^2+b^2)=z^2/|z|^2=(z/|z|)^2\]

right?

Thank you

Answer 3

Yes you got it

Answer 4

Ok thank youuu