Show that for any complex number z, |z| = |-z|. (Hint: Let z = a + bi.)

Answer 1

if z = a + b i
z^2 = a^2 + 2 a b i + b^2 i^2
= a^2 + 2 a b i - b^2

if z = -a - bi
z^2 = a^2 + 2 a b i + b^2 i^2
= a^2 + 2 a b i -b^2