1. **Stating the problem:**
We are asked to find the value of the expression $$\frac{|z_2|}{|z_1|}$$ where $z_1$ and $z_2$ are complex numbers.
2. **Formula and rules:**
The modulus (or absolute value) of a complex number $z = a + bi$ is given by $$|z| = \sqrt{a^2 + b^2}$$ where $a$ is the real part and $b$ is the imaginary part.
3. **Intermediate work:**
- Calculate $|z_2|$ by finding the square root of the sum of squares of its real and imaginary parts.
- Calculate $|z_1|$ similarly.
- Then compute the fraction $$\frac{|z_2|}{|z_1|}$$.
4. **Simplification:**
If possible, simplify the fraction by canceling common factors.
5. **Explanation:**
The modulus represents the distance of the complex number from the origin in the complex plane. Dividing the moduli gives the ratio of these distances.
Since no specific values for $z_1$ and $z_2$ are given, the expression remains $$\frac{|z_2|}{|z_1|}$$ as the final answer.
Modulus Ratio 643040
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.