The common difference of the argument of the values of $(1 + i \sqrt{3})^{1 / 5}$ is

\frac{π}{5}

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\frac{2 π}{5}

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\frac{3 π}{5}

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\frac{4 π}{5}

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Solution

The correct option is A $\frac{2 π}{5}$
$(1 + i \sqrt{3})^{1 / 5} = 2^{1 / 5} e^{i (2 k π + \frac{π}{3}) \times \frac{1}{5}}$
$= 2^{1 / 5} e^{i π / 15}, 2^{1 / 5} e^{i 7 π / 15}, 2^{1 / 5} e^{i \frac{13 π}{5}}$
diff $= \frac{6 π}{15}$ diff $= \frac{13 π}{15} - \frac{7 π}{15}$
$= \frac{2 π}{5} = \frac{6 π}{15}$

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