Question

Given that `z` is a complex number and that`|z|> 0` Show that `|z + 1|>=1`?

Answer 1

I don't think it's true. (Unless I'm misunderstanding.)

`abs (a+bi) = sqrt (a^2 +b^2)`

Let `z = -1/2 + 0i` Then `z+1 = 1/2 +0i`

`abs z =1/2 = abs (z+1)`