## anonymous one year ago 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))

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1. anonymous

Sorry it is (-1+isqrt3)

2. freckles

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

3. freckles

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

4. anonymous

I got B for my answer, is that right?

5. freckles

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