Express in the complax form if `z= (4-3i)(2+i)`

Answer

To express \( z = (4 - 3i)(2 + i) \) in the standard complex form \( z = a + bi \), we will follow these steps:

### Step 1: Expand the expression
We start by multiplying the two complex numbers:

\[ z = (4 - 3i)(2 + i) \]

Using the distributive property (also known as the FOIL method for binomials), we get:

\[ z = 4 \cdot 2 + 4 \cdot i - 3i \cdot 2 - 3i \cdot i \]

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

\[ z = 8 + 4i - 6i - 3i^2 \]

### Step 3: Substitute \( i^2 \) with \(-1\)
Recall that \( i^2 = -1 \). Therefore, we can substitute \(-3i^2\) with \(3\):

\[ z = 8 + 4i - 6i + 3 \]

### Step 4: Combine like terms
Now, we combine the real parts and the imaginary parts:

\[ z = (8 + 3) + (4i - 6i) \]

This simplifies to:

\[ z = 11 - 2i \]

### Final Result
Thus, the complex number in standard form is:

\[ z = 11 - 2i \]

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