The complex number has magnitude zero, but doesn't really have an angle. The angle of a complex number is defined by where the ray through the origin and the complex number intersects the unit circle.

So,  the argument of zero is undefined.

I hope you understand it.

Hello,

The set of all complex numbers is denoted C. If z=a+bi∈C then the Real Part of z is Re(z)=a, while the Imaginary Part of z is Im(z)=b.

In a set of complex numbers argument of 0 is considered as zero or undefined since it is completely imaginary and thus it is just a matter of convention.

I hope this helps!

All the best!