Use DeMoivre's theorem to find the indicated roots of the complex number.
Square roots of

Question

Use DeMoivre's theorem to find the indicated roots of the complex number. ​
Square roots of  ​

Quizplus · Accepted Answer

Using DeMoivre's theorem, we can find the square roots of $11e^{i	heta}$ by first finding the square roots of 11 and halving the angle $	heta$.
$\sqrt{11} \approx 3.3166$ and $	heta=acce6_1f44_acb7_9f49_df05cec1750c_TB7896_11$
So the first square root is approximately $3.3166e^{i\frac{	heta}{2}} \approx 1.6583e^{iacce6_1f44_d3ca_9f49_6f2aefc1829d_TB7896_11}$.
The second square root is found by adding $\pi$ to the angle and is approximately $1.6583e^{i(acce6_1f44_d3ca_9f49_6f2aefc1829d_TB7896_11+\pi)} \approx -1.6583e^{i(acce6_1f44_d3ca_9f49_0fdec1f3ed63_TB7896_11)}$.
Therefore, the best choice is C.

Use DeMoivre's Theorem to Find the Indicated Roots of the Complex