Question

Use DeMoivre's Theorem to write the complex number in trigonometric form.
(sqrt2 + I sqrt2)^3

Answer 1

@ zepdrix

Answer 2

@zepdrix

Answer 3

So we need 2 pieces of information:

The magnitude, \(\Large\rm r\), of our thing inside the brackets,
and the angle it forms \(\Large\rm \theta\).

Answer 4

So when we have the form:\[\Large\rm a+b\mathcal i\](Which we do)
Then the radius is given by:
\[\Large\rm r=\sqrt{a^2+b^2}\]

Answer 5

so that would be 2

Answer 6

Mmm ok good.

Answer 7

r=2

Answer 8

Recall that tangent is \(\Large\rm \dfrac{opposite}{adjacent}\)

What that means for us here is that the tangent of theta is the imaginary component (opposite side) over the real component (adjacent side).
\[\Large\rm \tan \theta=\frac{b}{a}\]

Answer 9

Website crashed again? :( ugh great...

Answer 10

that equals 1

Answer 11

@zepdrix you still there

Answer 12

\[\Large\rm \tan \theta=1\]Yes, good.
So how do we solve for theta?
What special angles does this correspond to?