4. Find the modulus, Iz], and argument, 0 , of the complex number. -1 + i
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Please show work in detail.
![**Problem 4**
**Objective:** Find the modulus, \( |z| \), and argument, \( \theta \), of the complex number.
**Complex Number Given:**
\[ -1 + \frac{\sqrt{3}}{3}i \]
**Instructions:**
- Begin by identifying the real and imaginary parts of the complex number.
- Calculate the modulus \( |z| \) using the formula:
\[
|z| = \sqrt{a^2 + b^2}
\]
where \( a \) is the real part, and \( b \) is the imaginary part.
- Determine the argument \( \theta \), which is the angle made with the positive real axis in the complex plane. Use the formula:
\[
\theta = \tan^{-1}\left(\frac{b}{a}\right)
\]
Adjust the argument based on the quadrant in which the complex number is located.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6874e1f1-5298-4a44-ae8e-fa9c3662cb0d%2F0813f47d-fb9e-4f2f-b2fd-fd79b05bd9a6%2Fwb7pg2f_processed.png&w=3840&q=75)
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