Question

Find the fourth roots of 256(cos 240° + i sin 240°).

Answer 1

Answer with Step-by-step explanation:

We are given that

We have to find the fourth roots of given complex number.

$(256)^{\frac{1}{4}}=(4^4)^{\frac{1}{4}}=4^^{\frac{1}{4}\times 4}=4$

By using the formula

$(a^b)^x=a^{bx}$

$\theta=240^{\circ}$

$\theta=\frac{240}{4}=60^{\circ}$

Angle of rotation=$\frac{360}{4}=90^{\circ}$

Therefore, the four roots of given complex number are

$4(cos 60^{\circ}+i sin60^{\circ})$

$4(cos150^{\circ}+i sin150^{\circ})$

$4(cos240^{\circ}+isin 240^{\circ})$

$4(cos330^{\circ}+i sin330^{\circ})$