Express each of the following in the form b or bi, where b is a real number
`(1)/(2) sqrt((-3)/(4))`

Answer

To express the given expression \(\frac{1}{2} \sqrt{\frac{-3}{4}}\) in the form \(b\) or \(bi\), where \(b\) is a real number, we can follow these steps:

### Step 1: Simplify the square root
We start with the expression:
\[ \frac{1}{2} \sqrt{\frac{-3}{4}} \]
Since the square root of a negative number involves the imaginary unit \(i\), we can rewrite it as:
\[ \sqrt{\frac{-3}{4}} = \sqrt{\frac{3}{4}} \cdot \sqrt{-1} = \frac{\sqrt{3}}{2} \cdot i \]

### Step 2: Substitute back into the expression
Now, we substitute this back into our original expression:
\[ \frac{1}{2} \cdot \frac{\sqrt{3}}{2} \cdot i \]

### Step 3: Multiply the coefficients
Now, we multiply the coefficients:
\[ \frac{1 \cdot \sqrt{3}}{2 \cdot 2} \cdot i = \frac{\sqrt{3}}{4} \cdot i \]

### Final Result
Thus, the expression \(\frac{1}{2} \sqrt{\frac{-3}{4}}\) can be expressed in the form \(bi\) as:
\[ \frac{\sqrt{3}}{4} i \]

### Summary
In this case, \(b = \frac{\sqrt{3}}{4}\).

---