SOLUTION: Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form. (cos'pi'/5 + i sin 'pi'/5)^15

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form. (cos'pi'/5 + i sin 'pi'/5)^15      Log On


   

Question 1187641: Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.
(cos'pi'/5 + i sin 'pi'/5)^15
Answer by Alan3354(69443) About Me  (Show Source):
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Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.
(cos'pi'/5 + i sin 'pi'/5)^15
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(cos(pi/5) + i sin(pi/5))^15 = (1cis(pi/5)^15 = 1^15cis(15*pi/5)
= cis(3pi)
= cis(pi) = cos(pi) + i*sin(pi) = -1 + 0
= -1