Discussion
Let \(z = 1 + \dfrac{1}{i}\).Then the value of \(z^{4}\) is equal to
Answer: B
\(z^{4} = \) -4.
Since \(\frac{1}{i} = \frac{i}{i^{2}} = -i\), we have \(z = 1 - i\). Then
\[ \begin{aligned} z^{2} &= (1 - i)^{2} = 1 - 2i + i^{2} = -2i \\ z^{4} &= (-2i)^{2} = 4i^{2} = -4 \end{aligned} \]
Taking \(\frac{1}{i} = i\) by mistake gives \(z = 1 + i\), whose fourth power is also -4, but the options \(1 - i\) and \(1 + i\) are just \(z\) itself or its conjugate, not \(z^{4}\). The value 4 comes from dropping the sign of \(i^{2}\).
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