If z is a non -zero complex number then `(|barz|^(2))/(zbarz)` is equal to

Options

A. `(|barz|)/|z|`
B. `|barz|`
C. z
D. none of these

Answer

To solve the problem, we need to simplify the expression \(\frac{|z|^2}{z \bar{z}}\) where \(z\) is a non-zero complex number.

### Step-by-step Solution:

1. **Understanding the Components**:
- Let \(z\) be a complex number, which can be expressed as \(z = a + bi\) where \(a\) and \(b\) are real numbers.
- The conjugate of \(z\) is denoted as \(\bar{z} = a - bi\).
- The modulus of \(z\) is given by \(|z| = \sqrt{a^2 + b^2}\).

2. **Calculating \(|z|^2\)**:
- The modulus squared is \(|z|^2 = (|z|)^2 = a^2 + b^2\).

3. **Calculating \(z \bar{z}\)**:
- The product \(z \bar{z} = (a + bi)(a - bi) = a^2 + b^2 = |z|^2\).

4. **Substituting into the Expression**:
- Now we substitute \(|z|^2\) and \(z \bar{z}\) into the expression:
\[ \frac{|z|^2}{z \bar{z}} = \frac{|z|^2}{|z|^2} \]

5. **Simplifying the Expression**:
- Since \(|z|^2\) is non-zero (as \(z\) is a non-zero complex number), we can simplify:
\[ \frac{|z|^2}{|z|^2} = 1 \]

6. **Final Result**:
- Therefore, the expression \(\frac{|z|^2}{z \bar{z}}\) simplifies to \(1\).

### Conclusion:
The answer to the question is \(1\), which corresponds to option \(d\) (none of these) since none of the provided options matches the result.