Express in the complex form `z= (7-i)( 2+i)`

Answer

To express \( z = (7 - i)(2 + i) \) in complex form, we will follow these steps:

### Step 1: Expand the expression
We start by expanding the product using the distributive property (also known as the FOIL method for binomials):

\[ z = (7 - i)(2 + i) = 7 \cdot 2 + 7 \cdot i - i \cdot 2 - i \cdot i \]

### Step 2: Calculate each term
Now we calculate each term:

1. \( 7 \cdot 2 = 14 \)
2. \( 7 \cdot i = 7i \)
3. \( -i \cdot 2 = -2i \)
4. \( -i \cdot i = -i^2 \)

Since \( i^2 = -1 \), we have:

\[ -i \cdot i = -(-1) = 1 \]

### Step 3: Combine the terms
Now we combine all the terms we calculated:

\[ z = 14 + 7i - 2i + 1 \]

### Step 4: Simplify the expression
Combine the real parts and the imaginary parts:

1. Real part: \( 14 + 1 = 15 \)
2. Imaginary part: \( 7i - 2i = 5i \)

Thus, we have:

\[ z = 15 + 5i \]

### Final Result
The complex form of \( z \) is:

\[ z = 15 + 5i \]

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