The conjugate of the complex number represented by the point ( 6-5) is

Options

A. `6-5i`
B. ` 6+5i`
C. `-6+5i`
D. `-6-5i`

Answer

To find the conjugate of the complex number represented by the point (6, -5), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Complex Number**:
The point (6, -5) corresponds to a complex number where the real part is 6 and the imaginary part is -5. Therefore, we can express the complex number \( z \) as:
\[ z = 6 - 5i \]

2. **Define the Conjugate**:
The conjugate of a complex number \( z = a + bi \) is given by \( \overline{z} = a - bi \). In our case, since the imaginary part is negative, we will switch the sign of the imaginary part.

3. **Calculate the Conjugate**:
For our complex number \( z = 6 - 5i \), the conjugate \( \overline{z} \) will be:
\[ \overline{z} = 6 + 5i \]

4. **Final Result**:
Thus, the conjugate of the complex number represented by the point (6, -5) is:
\[ \overline{z} = 6 + 5i \]

### Final Answer:
The conjugate of the complex number represented by the point (6, -5) is \( 6 + 5i \).

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