Question

let z=x+iy, showing details, find in terms of x and y:
1. Re[(z/barz), limz/z)

Answer 1

\[z=x+iy,z ^{2}=\left( x+iotay \right)^{2}=x ^{2}+\iota ^{2}y ^{2}-\iota2xy=x ^{2}-y ^{2}-\iota2xy\]
\[\left( 1+\iota \right)^{2}==1+\iota ^{2}+2\iota=1-1+2\iota=2\iota \]
\[\left( 1+\iota \right)^{4}=\left( 2\iota \right)^{2}=4\iota ^{2}=-4\]
\[\left( 1+\iota \right)^{16}=\left( -4 \right)^{4}=256\]
(1+i)^16 z^2=256[(x^2-y^2)-i2xy]
\[\mathbb{R} \left[ \left( 1+i \right)^{16}z ^{2} \right]=256\left( x ^{2} -y ^{2}\right)\]

Answer 2

thanks

Answer 3

but how did -i2xy dissapear

Answer 4

please

Answer 5

2. Re(z/barz), lim(z/z)
barz is conjugate of z.