On the set `C` of all complex numbers an operation `'o'` is defined by `z_1\ o\ z_2=sqrt(z_1z_2)` for all `z_1,\ z_2 in C` . Is `o` a binary operation on `C` ?

Explanation

To determine whether the operation \( o \) defined by \( z_1 \ o \ z_2 = \sqrt{z_1 z_2} \) is a binary operation on the set \( C \) of all complex numbers, we need to check the closure property of the operation. A binary operation on a set is defined as an operation that takes two elements from the set and produces another element that is also in the same set.

### Step-by-Step Solution:

1. **Understanding the Operation**:
The operation \( o \) is defined as:
\[
z_1 \ o \ z_2 = \sqrt{z_1 z_2}
...