Write the conjugate of
`sqrt(-16)-3`

Answer

To find the conjugate of the expression \( \sqrt{-16} - 3 \), we will follow these steps:

### Step 1: Simplify \( \sqrt{-16} \)
The square root of a negative number can be expressed using the imaginary unit \( i \), where \( i = \sqrt{-1} \). Therefore, we can rewrite \( \sqrt{-16} \) as:
\[ \sqrt{-16} = \sqrt{16} \cdot \sqrt{-1} = 4i \]

### Step 2: Substitute back into the expression
Now we can substitute \( \sqrt{-16} \) back into the original expression:
\[ \sqrt{-16} - 3 = 4i - 3 \]

### Step 3: Identify the real and imaginary parts
In the expression \( 4i - 3 \), we can identify the real part \( a \) and the imaginary part \( b \):
- Real part \( a = -3 \)
- Imaginary part \( b = 4 \)

### Step 4: Write the complex number in standard form
We can express the complex number in standard form \( z = a + ib \):
\[ z = -3 + 4i \]

### Step 5: Find the conjugate
The conjugate of a complex number \( z = a + ib \) is given by \( \overline{z} = a - ib \). Therefore, the conjugate of our complex number is:
\[ \overline{z} = -3 - 4i \]

### Final Answer
Thus, the conjugate of \( \sqrt{-16} - 3 \) is:
\[ \overline{z} = -3 - 4i \]

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