Find the cube root of -125/2(1+sqrt3i).

Preston Walker

Preston Walker

Answered question

2023-02-12

Find the cube root of - 125 2 ( 1 + 3 i )

Answer & Explanation

klitternrms

klitternrms

Beginner2023-02-13Added 3 answers

- 125 2 ( 1 + 3 i ) = - 125 2 - 125 3 2 i = 125 e - 2 π 3 i
Cubic roots of - 125 2 ( 1 + 3 i ) is ( 125 e - 2 π 3 i ) 1 3 = 5 ( e i ( 2 k π - 2 π 3 ) ) 1 3 = 5 e i ( 2 k π 3 - 2 π 9 ) , k = 0 , 1 , 2
- 125 2 ( 1 + 3 i ) 3 = 5 e - 2 π i 9 ,   5 e - 4 π i 9 ,   5 e - 10 π i 9
Chana Rivera

Chana Rivera

Beginner2023-02-14Added 1 answers

Another variant of answers is - 5 ( cos ( - 5 π 9 ) + i sin ( - 5 π 9 ) ) , - 5 ( cos ( π 9 ) + i sin ( 5 π 9 ) ) , - 5 ( cos ( 7 π 9 ) + i sin ( 7 π 9 ) )

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