Find the complex conjugate fo the following
`(15 + 3i) - (4-20i)`

Answer

To find the complex conjugate of the expression \((15 + 3i) - (4 - 20i)\), we can follow these steps:

### Step 1: Simplify the expression
We start with the expression:
\[ (15 + 3i) - (4 - 20i) \]
Distributing the negative sign:
\[ 15 + 3i - 4 + 20i \]

### Step 2: Combine the real parts and the imaginary parts
Now, we combine the real parts (15 and -4) and the imaginary parts (3i and 20i):
\[ (15 - 4) + (3i + 20i) \]
Calculating the real part:
\[ 15 - 4 = 11 \]
Calculating the imaginary part:
\[ 3i + 20i = 23i \]
So, we have:
\[ 11 + 23i \]

### Step 3: Find the complex conjugate
The complex conjugate of a complex number \(z = x + yi\) is given by \(z^* = x - yi\). For our result \(11 + 23i\):
\[ z^* = 11 - 23i \]

### Final Answer
Thus, the complex conjugate of the expression \((15 + 3i) - (4 - 20i)\) is:
\[ \boxed{11 - 23i} \]

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