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**Find the complex number \( z \) such that \( |z| = -1 + i \)**

This is an interesting question because the magnitude (or modulus) of a complex number \( |z| \) must always be a non-negative real number, and the expression given \( |z| = -1 + i \) is a complex number itself, which raises a contradiction.

Typically, the modulus \( |z| \) of a complex number \( z = a + bi \) is defined as \( |z| = \sqrt{a^2 + b^2} \), which is always real and non-negative. Therefore, \( |z| = -1 + i \) doesn't seem to make sense as it equates a real, non-negative quantity to a complex number.

It is likely that there is a mistake in the problem. Could it be that the problem should have been written as:

- "Find the complex number \( z \) such that \( z = -1 + i \)"?

If this is the intended problem, the solution would simply be \( z = -1 + i \), since it's already specified.

Would you like further clarification on this or the concept of complex numbers and their modulus?

Here are 5 follow-up questions for deeper understanding:
1. What is the geometric interpretation of the modulus of a complex number?
2. How do you find the argument of a complex number like \( -1 + i \)?
3. Can the modulus of a complex number ever be negative?
4. How do you represent a complex number in polar form?
5. What are the applications of complex numbers in engineering and physics?

**Tip:** When dealing with the modulus of a complex number, remember that it always refers to the distance from the origin in the complex plane and is non-negative.

Find complex number such that |z| = -1 + i

Explore the mathematical concepts of complex numbers and their modulus. This problem discusses the non-negative property of the modulus and examines potential errors in the given equation |z| = -1 + i.

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