write in rectangular form

(square root 2-i) 4th power

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- Nov 15th 2006, 12:41 AMSHORTYdemoivre theorem
write in rectangular form

(square root 2-i) 4th power - Nov 15th 2006, 05:41 AMtopsquark
Do you mean ?

We need to rationalize this before we can work with it, so:

=

=

=

So we need to know what is.

Note that .

So

Dividing the two equations gives:

So

rad.

Squaring the two equations and adding gives:

.

Thus .

By DeMoivre's theorem:

So

=

=

= <-- These are apparently exact, though I don't know how to prove it.

So finally:

=

-Dan