Question

Ex. 3:
Solve x?=1 (using De Moivre's Theorem)​

Answer 1

Step-by-step explanation:

For integer k,

z4=1+0i

=cos(2πk)+isin(2πk)

=cos(4(π2k))+isin(4(π2k))

=(cos(π2k)+isin(π2k))4

z=cos(π2k)+isin(π2k)

That’s four different values, given by any four consecutive k :

k=0,z=cos0+isin0=1

k=1,z=cosπ2+isinπ2=i

k=2,z=cosπ+isinπ=−1

k=3,z=cos3π2+isin3π2=−i