ashnaernay03
ashnaernay03 ashnaernay03
  • 12-04-2021
  • Mathematics
contestada

PLEASE HELP!!!

(64i)^1/6

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

Respuesta :

sqdancefan
sqdancefan sqdancefan
  • 13-04-2021

9514 1404 393

Answer:

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

Step-by-step 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

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