To find the real part of \(\frac{2 - 3 + 4 - 5 + 6}{1 - i}\), let's break it down step by step:

### Step 1: Simplify the numerator
\[
2 - 3 + 4 - 5 + 6 = 4
\]

### Step 2: Write the expression as a fraction
\[
\frac{4}{1 - i}
\]

### Step 3: Multiply the numerator and denominator by the complex conjugate of \(1 - i\)
The conjugate of \(1 - i\) is \(1 + i\). So, we multiply both the numerator and the denominator by \(1 + i\):
\[
\frac{4}{1 - i} \times \frac{1 + i}{1 + i} = \frac{4(1 + i)}{(1 - i)(1 + i)}
\]

### Step 4: Simplify the denominator
\[
(1 - i)(1 + i) = 1^2 - i^2 = 1 - (-1) = 2
\]

### Step 5: Simplify the expression
\[
\frac{4(1 + i)}{2} = 2(1 + i)
\]

### Step 6: Find the real part
The real part of \(2(1 + i)\) is \(2\).

### Final Answer:
The real part of \(\frac{2 - 3 + 4 - 5 + 6}{1 - i}\) is **2**.

Do you want more details or have any questions?

Here are 5 related questions:
1. How do you find the imaginary part of the same expression?
2. What is the modulus of a complex number?
3. How do you multiply two complex numbers?
4. What is the polar form of a complex number?
5. How do you divide two complex numbers?

**Tip:** Always multiply by the conjugate to simplify complex fractions.

What is the real part of (2-3+4-5+6)/1-i?

Discover how to find the real part of (2-3+4-5+6)/(1-i) using complex number conjugates and simplification techniques. This guide is suitable for students in Grades 10-12, covering important concepts in complex numbers and algebra.

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