Math, asked by slalita941, 3 months ago

Find all possible values of (1+i)1/3 and obtain
their product.


Answers

Answered by patel28881
0

Answer:

+i=

3

)

=2

2

1

+i

2

3

=2[cos(

3

π

)+isin(

3

π

)]

Here, r=2,ϕ=arg(z)=π/3,n=5

n

th

roots are given by r

1/5

[cos(

n

ϕ+2kπ

)+isin(

n

ϕ+2kπ

)]

z

0

=2

1/5

5

cos

3

π

+2(0)π

+i

5

sin

3

π

+2(0)π

z

0

=2

1/5

(cos

15

π

+isin

15

π

)

z

1

=2

1/5

5

cos

3

π

+2π

+

5

isin

3

π

+2π

=2

1/5

cos

15

+isin

15

]

z

2

=2

1/5

5

cos

3

π

+4π

+

5

isin

3

π

+4π

=2

1/5

cos

15

13π

+isin

15

]

z

3

=2

1/5

[cos

15

19π

+isin

15

19π

] [ putting k=3 ]

z

4

=2

1/5

[cos

15

25π

+isin

15

25π

] [ putting k=4 ]

z

4

=2

1/5

cos

3

+isin

3

z

0

,z

1

,z

2

,z

3

,z

4

are the fifth roots of given complex no.

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