Question

Find the cube roots of 27(cos 279° + i sin 279°).

Answer 1

Answer:

3 (cos 93 + i sin 93)

Step-by-step explanation:

We are to find the cube roots of the following:

27 (cos 279° + i sin 279°)

$(cosx + i sin x) = cos (nx)) + i sin (nx)$

$27 \times (cos 279+i sin 279)\frac{1}{3} =27\frac{1}{3} \times (cos 279+i sin 279)\frac{1}{3}$

Simplifying this to get:

$3\times (cos279+i sin279)\frac{1}{3}$

$3\times(cos 279+i sin 279)13=3(cos \frac{279}{3} +i sin \frac{279}{3})$

We know that $\frac{279}{3}=3$

So, cube root = $3(cos 93 + i sin 93)$