What is the value of \frac{1}{2}+\text{Re}\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. 0 ✓
- C. 1
- D. 2
Correct Answer: B. 0
Explanation
From the quadratic equation, Z_1/Z_2 is either \omega or \omega^2. The real part of both \omega and \omega^2 is -1/2. Substituting this gives 1/2 + (-1/2) = 0.
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