Question

Which expression is a sixth root of (-1+sqrt3)?

A. 6sqrt2 (cos90) +isin(90))
B. 6sqrt2 (cos300) +isin(300))
C. 6sqrt2 (cos60) +isin(60))
D. 6sqrt2 (cos20) +isin(20))

Answer 1

Sorry it is (-1+isqrt3)

Answer 2

Have you first tried to write (-1+sqrt(3)*i) in r(cos(theta)+isin(theta)) form?

Answer 3

or I guess instead of finding all 6th roots you go go another way
you could raise your choices to the 6th power and see which gives you -1+sqrt(3)*i

Answer 4

I got B for my answer, is that right?

Answer 5

well let's check:
\[(\sqrt[6]{2}(\cos(300)+i \sin(300))^6 \\ (\sqrt[6]{2})^6(\cos(300 \cdot 6)+i \sin(300 \cdot 6)) \\ 2^\frac{6}{6}(\cos(1800)+i \sin(1800)) \\ 2^1 (\cos(1800-4(360))+i \sin(1800-4(360)) \\ 2(\cos(360)+i \sin(360))\]
can you finish simplifying