Question

Prove that ( −1+√3 2 ) + ( −1−√3 2 ) has value -1, if = 3 ± 1 and 2 if = 3, where is an integer.

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Answer 1

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Class 11

>>Applied Mathematics

>>Number theory

>>Complex Numbers

>>If a = -1+i√(3)2 ,b = -1-i√(3)2 then sh

Question

Bookmark

If a=

2

−1+i

3

,b=

2

−1−i

3

then show that a

2

=b and b

2

=a.

Medium

Solution

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a=

2

−1+i

3

⇒a

2

=(

2

−1+i

3

)

2

=

4

1+3i

2

−2

3

i

=

4

1−3−2i

3

=

4

−2−2i

3

=

2

−1−i

3

=b

b=

2

−1−i

3

⇒b

2

=(

2

−1−i

3

)

2

=

4

1+3i

2

+2

3

i

=

4

1−3+2i

3

=

4

−2+2i

3

=

2

−1+i

3

=a