Question

how to prove \(\large (\overline{z})^n = \overline{z^n}\)

Answer 1

z is cmplex number
over bar refers to conjugate of z

Answer 2

right

Answer 3

certanly true for zconj^1

Answer 4

lets see if we can write one of those ladder +1 proofs

Answer 5

forget what the proof is called induction?

Answer 6

\(\large (\overline{z})^1 = \overline{z} = \overline{z^1}\)

so base n=1 is true

Answer 7

are we trying induction ?

Answer 8

yeah lets try it

Answer 9

okay

Answer 10

assuming \(\large (\overline{z})^n = \overline{z^n}\) is true,
we need to show \(\large (\overline{z})^{n+1} = \overline{z^{n+1}}\)

Answer 11

yeah

Answer 12

i dunno geometrically it kinda just makes sense