You can
put this solution on YOUR website!First you have to convert
into polar form
+i\sin(\theta)\right))
.
To do that, use the formulas
and
)
In this case, we're given
which means that
and
. So
and
=\tan^{-1}\left(1\right)=\frac{\pi}{4})
So this means that the rectangular expression
is equivalent to the polar form
+i\sin(\frac{\pi}{4})\right))
.
From here, we can now use De Moivre's Theorem. De Moivre's Theorem states that if
, then
+i\sin(n\theta)\right))
Since
, using De Moivre's Theorem gets us
^{12}\left(\cos(12*\frac{\pi}{4})+i\sin(12*\frac{\pi}{4})\right))
+i\sin(3\pi)\right))
... Evaluate
to the 12th power to get
+i\sin(3\pi)\right))
... Evaluate 2 to the 6th power to get 64
)
... Evaluate the trig functions.
)
... Simplify.
... Multiply
Because we let
, this means that
(