Math Problem Statement

Give me the correct answer

Si z_1 = -9 + 2i y z_2 = 8 - 3i entonces || z_1 / z_2 || es:

Solution

The modulus (or norm) of z1z2\frac{z_1}{z_2} is approximately 1.0791.079. This corresponds to the value:

8573 unidades\frac{\sqrt{85}}{73} \text{ unidades}

Thus, the correct answer is b. 8573\frac{\sqrt{85}}{73} unidades.

Would you like further details or have any questions?

Here are 5 related questions you might find interesting:

  1. How do you calculate the modulus of a complex number?
  2. What are the real and imaginary parts of a complex number?
  3. How do you multiply or divide complex numbers?
  4. What is the geometric interpretation of dividing two complex numbers?
  5. Can we generalize this process for other complex number operations?

Tip: When dividing complex numbers, remember to multiply both the numerator and denominator by the conjugate of the denominator to simplify the expression.

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Modulus
Division of Complex Numbers

Formulas

Modulus of a complex number: |z| = sqrt(a^2 + b^2) for z = a + bi
Division of complex numbers: z_1 / z_2 = (z_1 * conjugate(z_2)) / |z_2|^2

Theorems

Pythagorean theorem (used to compute the modulus of a complex number)

Suitable Grade Level

Grades 11-12