Question

If n is an integer then show that (1+i) + (1-i)= 2n+1 cos npi/3

Answer 1

Answer:

(1+i)=

2

(cos

4

π

+sin

4

π

)

1−i=

2

(cos

4

π

−sin

4

π

)

(1+i)

2n

=(

2

)

2n

(cos(

4

2nπ

)+isin(

4

2nπ

))

(1−i)

2n

=(

2

)

2n

[cos(

4

2nπ

)−isin(

4

2nπ

)]

Adding (1+i)

2n

+(1−i)

2n

=(

2

)

2n

[2cos(

4

2nπ

)]

=2

n

2n

.2

1

cos(

2

nπ

)

=2

n+1

cos(

2

2nπ

)

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