Aspire Faculty ID #15385 · Topic: MAH MCA CET 2023 · Just now
MAH MCA CET 2023

$a = z^2 + z + 1$ where $z$ be the complex polarizing number, then what is not the value of $a$?

Solution

Let $z = e^{i\theta}$, then $a = 1 + e^{i\theta} + e^{2i\theta} = \dfrac{\sin(3\theta/2)}{\sin(\theta/2)} e^{i\theta}$. After simplification, the value $\dfrac{1}{3}$ is not possible.
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