Question

Find all z in C which satisfy z conjugate = z^2

Answer 1

Note C=Complex (x+iy)

Answer 2

@sat
http://openstudy.com/#/updates/4ed58b7be4b0bcd98ca6ebe8

Answer 3

0 works
1 works
i don't think anything else works.
\[(a+bi)^2=a^2-b^2+(2ab)i\] so this would mean you would have to solve
\[a=a^2-b^2\] and
\[b=2ab\]

Answer 4

sorry it is
\[\overline{z }= z^2\] so it would be
\[a=a^2-b^2\]and
\[-b=2ab\] but the outcome is still the same

Answer 5

i got a=-1/2 and b=\[\sqrt{3}/2\]