Question

how to find z⁵=i by demoivre's theorem?​

Answer 1

Step-by-step explanation:

Let z=r(cos(θ)+isin(θ)) be a complex number and n any integer. Then.

zn=(rn)(cos(nθ)+isin(nθ))

Let n be a positive integer. The nth roots of the complex number r[cos(θ)+isin(θ)] are given by.

With this, we have another proof of De Moivre's theorem that directly follows from the multiplication of complex numbers in polar form. Show that cos ⁡ ( 5 θ ) = c o s 5 θ − 10 cos ⁡ 3 θ sin ⁡ 2 θ + 5 cos ⁡ θ sin ⁡ 4 θ