`if A=[{:(1+i,-2i),(7,3-i):}]and B=[{:(1-i,2i),(-3,3+i):}],`then find A+B. `

Explanation

To find the sum of the matrices A and B, we will add the corresponding elements of each matrix. Let's break it down step by step.

Given:
\[ A = \begin{pmatrix} 1+i & -2i \\ 7 & 3-i \end{pmatrix} \]
\[ B = \begin{pmatrix} 1-i & 2i \\ -3 & 3+i \end{pmatrix} \]

### Step 1: Identify the elements of matrices A and B
- The elements of matrix A are:
- \( A_{11} = 1+i \)
- \( A_{12} = -2i \)
- \( A_{21} = 7 \)
- \( A_{22} = 3-i \)

- The elements of matrix B are:
- \( B_{11} = 1-i \)
- \( B_{12} = 2i \)
- \( B_{21} = -3 \)
- \( B_{22} = 3+i \)

### Step 2: Add the corresponding elements
Now we will add the corresponding elements from matrices A and B.

1. **First Row, First Column:**
\[ A_{11} + B_{11} = (1+i) + (1-i) = 1 + i + 1 - i = 2 \]

2. **First Row, Second Column:**
\[ A_{12} + B_{12} = (-2i) + (2i) = -2i + 2i = 0 \]

3. **Second Row, First Column:**
\[ A_{21} + B_{21} = 7 + (-3) = 7 - 3 = 4 \]

4. **Second Row, Second Column:**
\[ A_{22} + B_{22} = (3-i) + (3+i) = 3 - i + 3 + i = 6 \]

### Step 3: Write the resulting matrix
Now we can write the resulting matrix A + B:
\[ A + B = \begin{pmatrix} 2 & 0 \\ 4 & 6 \end{pmatrix} \]

### Final Answer
Thus, the sum of matrices A and B is:
\[ A + B = \begin{pmatrix} 2 & 0 \\ 4 & 6 \end{pmatrix} \]

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