Answer with Step-by-step explanation:
We are given that
We have to find the fourth roots of given complex number.
[tex](256)^{\frac{1}{4}}=(4^4)^{\frac{1}{4}}=4^^{\frac{1}{4}\times 4}=4[/tex]
By using the formula
[tex](a^b)^x=a^{bx}[/tex]
[tex]\theta=240^{\circ}[/tex]
[tex]\theta=\frac{240}{4}=60^{\circ}[/tex]
Angle of rotation=[tex]\frac{360}{4}=90^{\circ}[/tex]
Therefore, the four roots of given complex number are
[tex]4(cos 60^{\circ}+i sin60^{\circ})[/tex]
[tex]4(cos150^{\circ}+i sin150^{\circ})[/tex]
[tex]4(cos240^{\circ}+isin 240^{\circ})[/tex]
[tex]4(cos330^{\circ}+i sin330^{\circ})[/tex]
