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

Question

Quizplus · Accepted Answer

To use DeMoivre's Theorem, we first need to convert the complex number to polar form:
$11e^{b+\frac{\pi}{4}}$

To find the 5th power of this complex number, we simply raise the modulus to the 5th power and multiply the argument by 5:
$11^5e^{5b+\frac{5\pi}{4}}$

Simplifying this expression, we get:
$11e^{5b+\frac{\pi}{4}}$

The decimal representation of $5b$ is $2.40064225$, so we can convert this back to polar form as:
$11e^{2.40064225+\frac{\pi}{4}}$

Converting back to rectangular form, we get:
$11	imes 0.88368 + 11	imes 0.46812i \approx 9.720 + 5.149i$

The best choice is D because it is the only answer that matches this rectangular form.

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