What is the value of \left|\frac{Z_{1}}{Z_{2}}\right|?
Direction: Consider the following for the two (02) items that follow :<br>Let Z_{1} and Z_{2} be any two complex numbers such that Z_{1}^{2}+Z_{2}^{2}+Z_{1}Z_{2}=0.
- A. 1 ✓
- B. 2
- C. 3
- D. 4
Correct Answer: A. 1
Explanation
Dividing the given equation by Z_2^2 yields (Z_1/Z_2)^2 + (Z_1/Z_2) + 1 = 0. The roots of this equation are the non-real cube roots of unity, \omega and \omega^2. The modulus of both \omega and \omega^2 is 1. Therefore, |Z_1/Z_2| = 1.
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