Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.

Question

Quizplus · Accepted Answer

Using DeMoivre's theorem:
$(e^{i	heta})^{10} = e^{10i	heta}$
where $	heta = \angle(11eb11e8\_19dc\_aeed\_ad38\_f56f34371de1\_TB4588\_00)$
We can convert the complex number to polar form:
$z = 2\sqrt{5}e^{i\arctan(5/7)}$
Now, applying DeMoivre's theorem:
$z^{10} = (2\sqrt{5})^{10}e^{i10\arctan(5/7)}$
Using the identity that $	an(2	heta) = \frac{2	an(	heta)}{1-	an^2(	heta)}$,
we can derive that $	an(10\arctan(5/7)) = -\frac{120}{119}$.
Therefore, the answer is $11ec826f\_40b0\_c565\_9e7c\_dd25f8e6b314\_TB4588\_00$.

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