Question

If z = 1+i, find z^2 and 1/z. Also, plot the Argand diagram for both.

Answer 1

If $z = 1+i$, let us find $z^2$ and $\frac{1}{z}:$

$z^2=(1+i)^2=1+2i+i^2=1+2i-1=2i,$

$\frac{1}z=\frac{1}{1+i}=\frac{1-i}{(1+i)(1-i)}=\frac{1-i}{2}=\frac{1}2-\frac{1}2i.$

Also, let us plot the Argand diagram for both: