Question

I GIVE MEDALS
Find the fifth roots of 243(cos 300° + i sin 300°).

Answer 1

Thats the question I was given though

Answer 2

243(cos300+isin300)
\[\left( 243 \right)^{\frac{ 1 }{ 5 }}\left( \cos 300+isin300 \right)^{\frac{ 1 }{ 5 }}\]
\[=\left( 3^{5} \right)^{\frac{ 1 }{ 5 }}\left( \cos \frac{ 300 }{5 }+isin \frac{ 300 }{5 }\right) \]
\[=3^{5\times \frac{ 1 }{ 5 }}\left( \cos 60+i \sin 60 \right)\]
\[=3\left( \frac{ 1 }{ 2 }+i \frac{\sqrt{3} }{ 2 } \right)\]
Here i have used de moivre's theorem.

Answer 3

The Last part is te fifth root @surjithayer ?

Answer 4

since 360/5 = 72,

245(cos 300+ i sin300)
245(cos 12+ i sin12)
245(cos 84+ i sin84)
245(cos 156+ i sin156)
245(cos 228+ i sin228)

Answer 5

THANK YOU OMG

Answer 6

yes

Answer 7

@amistre64 but why is is 245 and not 243?

Answer 8

becuase i hit the wrong key ....

Answer 9

Oh okay whew lol

Answer 10

:)