Complex conjugate of 3i-4 is:

Options

A. `3i+4`
B. `-3i-4`
C. `-3i+4`
D. none of these

Answer

To find the complex conjugate of the complex number \(3i - 4\), we can follow these steps:

### Step 1: Identify the real and imaginary parts
The given complex number is \(3i - 4\). We can rewrite this in the standard form of a complex number, which is \(x + yi\), where \(x\) is the real part and \(y\) is the imaginary part.

Here, we can see:
- The real part \(x = -4\)
- The imaginary part \(y = 3\)

### Step 2: Apply the formula for the complex conjugate
The formula for the complex conjugate of a complex number \(z = x + yi\) is given by:
\[ \overline{z} = x - yi \]

### Step 3: Substitute the values
Now, substituting the values of \(x\) and \(y\) into the formula:
\[ \overline{z} = -4 - 3i \]

### Step 4: Write the final answer
Thus, the complex conjugate of \(3i - 4\) is:
\[ -4 - 3i \]

### Summary
The complex conjugate of \(3i - 4\) is \(-4 - 3i\).

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