Question

One of the values of \[ (\sqrt{3}-i)^{5/3} \] is:

• A. \( 2^{5/3} \text{cis} \frac{5\pi}{18} \)
• B. \( 2^{5/3} \text{cis} \frac{19\pi}{18} \)
• C. \( 2^{5/3} \text{cis} \frac{23\pi}{18} \)
• D. \( 2^{5/3} \text{cis} \frac{17\pi}{18} \)

Hint:

When options are given in "cis" form, first find the basic argument. If it doesn't match, add \( 2\pi \) (or multiples) to the internal angle before multiplying by the power to find the branch that matches the choices.

Answer 1

The Correct Option is B