Use DeMoivre's Theorem to find the indicated power of the following complex number.
A)16,384
B)1,048,576
C)32,768
D)-16,384
E)262,144

Question

Use DeMoivre's Theorem to find the indicated power of the following complex number. 
A)16,384 
B)1,048,576 
C)32,768 
D)-16,384 
E)262,144

Quizplus · Accepted Answer

Using DeMoivre's Theorem, we can find the power of a complex number expressed in polar form. We first need to convert the given complex number into polar form:
11eb80b1_af82_70e0_a291_4f16d1de9d9b_TB8633_11 = 11(cos(80°) + i sin(80°))
To find the 4th power of this complex number, we can raise the modulus to the 4th power and multiply the argument by 4:
(11)^4 (cos(4*80°) + i sin(4*80°)) = 14641(cos(320°) + i sin(320°)) = -16,384 - 0i
Therefore, the answer is D, -16,384.

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