What is the trigonometric form of the complex variable $z=0+0i $?

$\begingroup$

I'm confused how do i determine the trigonometric form of the complex variable $z=0+0i$ , it has modula such that is 0 but what about it's argument ?

Note : At a least i would like to know it's geometric intrepretation

Thank you for any help

$\endgroup$ 4

2 Answers

$\begingroup$

The trigonometric representation of a complex number is $r(cos(\theta)+ i sin(\theta))$. For 0, r= 0 and $\theta$ becomes irrelevant.

$\endgroup$ 1 $\begingroup$

It's just $z=0$. For any $\phi$, we have $$z=0e^{i\phi}=0(cos\phi+i\sin\phi) = 0$$

You can think of this as the zero vector. It is trivially unaffected by rotation. We can add any arbitrary phase to zero, and it remains zero.

$\endgroup$ 3