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

Solution:

Given 243(cos 260° + i sin 260°)

Using De- Moivers theorem, 

cosa + isina = e^ia and (e^ia)^b = e^iab = cosab + isinab

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

= (3⁵)^1/5(cos 260/5 + i sin 260/5)

= (3⁵)^1/5(cos 52 + i sin 52)

= 3(0.62 + 0.79i)

= 1.86 + 2.37i

Therefore, the fifth root of 243(cos 260° + i sin 260°) is 1.86 + 2.37i

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

Summary:

The fifth root of 243(cos 260° + i sin 260°) is 1.86 + 2.37i