The conjugate of ` sqrt(-5) +3^(2)` is

Options

A. `9 -sqrt5i`
B. ` 9+sqrt5i`
C. ` -9+sqrt5i`
D. `-9-sqrt5i`

Answer

To find the conjugate of the expression \( \sqrt{-5} + 3^2 \), we can follow these steps:

### Step 1: Simplify the expression
First, we need to simplify \( 3^2 \):
\[ 3^2 = 9 \]
So, the expression becomes:
\[ \sqrt{-5} + 9 \]

### Step 2: Express \( \sqrt{-5} \) in terms of \( i \)
Next, we know that \( \sqrt{-5} \) can be expressed using the imaginary unit \( i \):
\[ \sqrt{-5} = \sqrt{5} \cdot \sqrt{-1} = \sqrt{5} \cdot i \]
Thus, we can rewrite the expression as:
\[ \sqrt{5} i + 9 \]

### Step 3: Rearrange the expression
We can rearrange the expression to highlight the real and imaginary parts:
\[ 9 + \sqrt{5} i \]

### Step 4: Find the conjugate
The conjugate of a complex number in the form \( a + bi \) is given by \( a - bi \). In our case, \( a = 9 \) and \( b = \sqrt{5} \). Therefore, the conjugate is:
\[ 9 - \sqrt{5} i \]

### Final Answer
Thus, the conjugate of \( \sqrt{-5} + 3^2 \) is:
\[ \boxed{9 - \sqrt{5} i} \]

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