The conjugate of the complex number `(a+ib)` is :

Options

A. `-a-ib`
B. `-a+ib`
C. `a-ib`
D. None of these

Answer

To find the conjugate of the complex number \( z = a + ib \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Complex Number**:
The given complex number is \( z = a + ib \), where \( a \) is the real part and \( b \) is the imaginary part.

2. **Define the Conjugate**:
The conjugate of a complex number \( z \) is denoted as \( \overline{z} \) and is defined as the real part minus the imaginary part.

3. **Apply the Definition**:
For the complex number \( z = a + ib \):
- The real part is \( a \).
- The imaginary part is \( b \).

Therefore, the conjugate \( \overline{z} \) can be expressed as:
\[ \overline{z} = \text{Real part} - i \times \text{Imaginary part} = a - ib \]

4. **Write the Final Answer**:
Thus, the conjugate of the complex number \( a + ib \) is:
\[ \overline{z} = a - ib \]

### Final Answer:
The conjugate of the complex number \( a + ib \) is \( a - ib \).

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