SOLUTIONS Task 1

Task 1

The de Moivre's Theorem is:

Let us take n=2, then
. We present the complex number 'z' in trigonometric form
and take the square of this number:

From the de Moivre's theorem it is equal to
:

Now we equate the Real and Imaginary parts of the above expression:

the Real parts

the Imaginary parts

The first of the above equations gives
.

Then
.

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