Question

PLEASE HELP!!!

(64i)^1/6

a) write answer in polar form
b) write answer in standard form

Answer 1

9514 1404 393

Answer:

• 2∠15°
• 2cos(15°) +i·2sin(15°) ≈ 1.93185 +0.517638i

Explanation:

Using Euler's formula, the 6th root is easily found.

(64i)^(1/6) = ((2^6)e^(iπ/2))^(1/6) = 2e^(iπ/12) = 2∠15°

= 2(cos(15°) +i·sin(15°)) = 2·cos(15°) +i·2·sin(15°) ≈ 1.93185 +0.517638i