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

##### 1 Answer
Apr 6, 2015

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

$\left\mid a + b i \right\mid = \sqrt{{a}^{2} + {b}^{2}}$

Let $z = - \frac{1}{2} + 0 i$ Then $z + 1 = \frac{1}{2} + 0 i$

$\left\mid z \right\mid = \frac{1}{2} = \left\mid z + 1 \right\mid$