Posted by britt on Tuesday, January 17, 2012 at 11:28am.
Use De Moivre’s Theorem to simplify each expression. Write the answer in the form a + bi.
{1  i(/3)}^4

trigonometry  Reiny, Tuesday, January 17, 2012 at 2:11pm
I will assume you know the theorem and the common variables used in it
r = √(1^2 + (1/3)^2 )
= √(1 + 1/9)
= √(10/9)
√10/3
let the angle be Ø
cosØ = 1/(√10/3) = 3/√10
sinØ = (1/3) / (√10/3) = 3/√10 , so Ø is in IV and Ø = 341.565°
so (1  (1/3) i )^4 = (√10/3)^4 [ cos 4(341.565° + i sin 4(341.564°)
= (100/81) [ .28 + (.96i) ]
= 28/81  96/81i
= 28/81  32/27 i
=
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