Let 
z
=
1
−
1
i

Calculate 
R
e
 
z
 (i.e., the real part of 
z
).

To calculate the real part of \( z = 1 - \frac{1}{i} \), we first simplify the expression.

1. Begin by rewriting \( \frac{1}{i} \) in a more manageable form:
   \[
   \frac{1}{i} = \frac{1}{i} \times \frac{i}{i} = \frac{i}{-1} = -i
   \]
   
   So, the expression for \( z \) becomes:
   \[
   z = 1 - (-i) = 1 + i
   \]

2. Now, the real part of \( z \), denoted as \( \text{Re}(z) \), is simply the real number part of \( z \).

Thus, the real part of \( z = 1 + i \) is:
\[
\text{Re}(z) = 1
\]

Would you like more details or have any questions?

---

Here are five related questions:
1. What is the imaginary part of \( z \)?
2. How do you represent \( z = 1 + i \) in polar form?
3. What is the modulus (absolute value) of \( z = 1 + i \)?
4. Can you compute the argument (angle) of \( z \) in radians?
5. How would you square \( z = 1 + i \)?

**Tip:** When dividing by \( i \), multiply by \( i/i \) to get rid of the imaginary unit in the denominator.

Let z = 1 - 1/i. Calculate Re z (i.e., the real part of z).

Learn how to calculate the real part of the complex number z = 1 - 1/i with a detailed step-by-step solution. This problem involves key concepts from complex numbers and algebra, and simplifies the expression to find Re(z). Suitable for students in Grades 10-12.

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