Find the fifth roots of 243(cos 260° + i sin 260°).

Question

Find the fifth roots of 243(cos 260° + i sin 260°).

Answer 1

This is the fist of five roots:

 

243^1/5(cos 260 + i sin 260)^1/5

3(cos 52 + i sin 52)

3(0.62 + 0.79i)

1.86 + 2.37i

 

The other four roots (calculated the same way) are:

 

3(cos 620 + i sin 620)^1/5

3(cos 980 + i sin 980)^1/5

3(cos 1340 + i sin 1340)^1/5

3(cos 1700 + i sin 1700)^1/5