De Moivre's Formula - Applications

Applications

This formula can be used to find the nth roots of a complex number. This application does not strictly use de Moivre's formula as the power is not an integer. However considering the right hand side to the power of n will, in each case, give the same value on the left-hand side.

If z is a complex number, written in polar form as

then

$z^{1/n} = \left^{1/n} = r^{1/n} \left$

where k is an integer. To get the n different roots of z one only needs to consider values of k from 0 to n − 1.

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