If w and z represents two complex numbers such that `w=3-2i and z=-2+4i`, which of he following gives `(w)/(2)` written in the form a+bi? (Note: `i^(2)=-1`)

Options

A. `-(3)/(2)-(1)/(2)i`
B. `-(7)/(10)-(2)/(5)i`
C. `(13)/(20)-(1)/(2)i`
D. `(7)/(6)+(2)/(3)i`

Answer

To solve the problem of finding \(\frac{w}{2}\) where \(w = 3 - 2i\), we will follow these steps:

### Step 1: Identify the complex number \(w\)
Given:
\[ w = 3 - 2i \]

### Step 2: Divide \(w\) by 2
To find \(\frac{w}{2}\), we divide both the real and imaginary parts of \(w\) by 2:
\[ \frac{w}{2} = \frac{3 - 2i}{2} = \frac{3}{2} - \frac{2i}{2} \]

### Step 3: Simplify the expression
This simplifies to:
\[ \frac{w}{2} = \frac{3}{2} - i \]

### Step 4: Write in the form \(a + bi\)
Here, we can express the result in the form \(a + bi\):
\[ \frac{w}{2} = \frac{3}{2} - 1i \]
Thus, \(a = \frac{3}{2}\) and \(b = -1\).

### Final Answer
The value of \(\frac{w}{2}\) in the form \(a + bi\) is:
\[ \frac{3}{2} - i \]

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