Question

Q7 Q18.) Write the roots in polar form with θ in degrees.

Answer 1

If
`z^3=64(\cos240^\circ+i\sin240^\circ)`, then


`z=64^(1/3)\bigg(\cos\frac{(240+360n)^\circ}3+i\sin\frac{(240+360n)^\circ}3\bigg)`

`z=4\bigg(\cos(80+120n)^\circ+i\sin(80+120n)^\circ\bigg)`

for
`n=0,1,2`. We get


`n=0\implies z=4(\cos80^\circ+i\sin80^\circ)`

`n=1\implies z=4(\cos200^\circ+i\sin200^\circ)`

`n=2\implies z=4(\cos320^\circ+i\sin320^\circ)`