Question

Find the cube roots of 125(cos 288° + i sin 288°).

cubed root(125*(cos(288)+ i sin (288))
cubed root(125)*cubed root(cos(288)+i sin(288))
5*(cos(288)+ i sin(288))^1/3

Answer 1

@jdoe0001

Answer 2

given
\[\large z=\rho(\cos\phi+i\sin\phi) \]
then the n n-th roots of z are given by:
\[\Large w_k=\sqrt[n]{\rho}\left[\cos\frac{\phi+2k\pi}{n}+i\sin\frac{\phi+2k\pi}{n}
\right] \]
with k=0,1,...,n-1

Answer 3

i just need to know how to finish it

Answer 4

cubed root(125*(cos(288)+ i sin (288))
cubed root(125)*cubed root(cos(288)+i sin(288))
5*(cos(288)+ i sin(288))^1/3

Answer 5

^^that is what i have so far

Answer 6

@helder_edwin

Answer 7

\[\Large w_0=\sqrt[3]{125}\left(\cos\frac{288}{3}+i\sin\frac{288}{3}\right) \]

Answer 8

u were doing it just fine. u need to apply now DeMoivre's formula to finish and get what i got.

Answer 9

but that is just the first of the three cubic roots of the given complex number

Answer 10

did u get it?

Answer 11

\(\large { \bf \sqrt[{\color{blue}{ 3}}]{\cfrac{288^o+{\color{brown}{ (2\pi \cdot 0)}}}{{\color{blue}{ 3}}}}\qquad \\\sqrt[{\color{blue}{ 3}}]{\cfrac{288^o+{\color{brown}{ (2\pi \cdot 1)}}}{{\color{blue}{ 3}}}}\qquad \\\sqrt[{\color{blue}{ 3}}]{\cfrac{288^o+{\color{brown}{ (2\pi \cdot 2)}}}{{\color{blue}{ 3}}}} }\)

Answer 12

well sorta missing a number there =) \(\bf \large {\sqrt[{\color{blue}{ 3}}]{125}\sqrt[{\color{blue}{ 3}}]{\cfrac{288^o+{\color{brown}{ (2\pi \cdot 0)}}}{{\color{blue}{ 3}}}}
\\ \quad \\
\sqrt[{\color{blue}{ 3}}]{125}\sqrt[{\color{blue}{ 3}}]{\cfrac{288^o+{\color{brown}{ (2\pi \cdot 1)}}}{{\color{blue}{ 3}}}}
\\ \quad \\
\sqrt[{\color{blue}{ 3}}]{125} \sqrt[{\color{blue}{ 3}}]{\cfrac{288^o+{\color{brown}{ (2\pi \cdot 2)}}}{{\color{blue}{ 3}}}} }\)

Answer 13

though \(2\pi\) should be replaced by 360º, since u r working with degrees.

Answer 14

i forgot to mention that. sorry.

Answer 15

yeap =)

Answer 16

\(\bf \large {\sqrt[{\color{blue}{ 3}}]{125}\sqrt[{\color{blue}{ 3}}]{\cfrac{288^o+{\color{brown}{ (360^o \cdot 0)}}}{{\color{blue}{ 3}}}}
\\ \quad \\
\sqrt[{\color{blue}{ 3}}]{125}\sqrt[{\color{blue}{ 3}}]{\cfrac{288^o+{\color{brown}{ (360^o \cdot 1)}}}{{\color{blue}{ 3}}}}
\\ \quad \\
\sqrt[{\color{blue}{ 3}}]{125} \sqrt[{\color{blue}{ 3}}]{\cfrac{288^o+{\color{brown}{ (360^o \cdot 2)}}}{{\color{blue}{ 3}}}} }\)

Answer 17

hehe

Answer 18

sorry i was eating dinner

Answer 19

22.9, 30, 34.7...are those the cubed roots? @jdoe0001 @helder_edwin