Q.1
If n be a + ive integer, then show that
(1+1)
where i = V-1
(1- i) 1-2
= 2 in-1
Answers
Answered by
2
Answer:
Let Z=
2
i
4n+1
−i
4n−1
=
2
[i
4n−1
.i
2
]−i
4n−1
=
2
i
4n−1
(i
2
−1)
=
2
i
4n−1
(−1−1)
…(i
2
=−1)
=−(i)
4n−1
=−(i)
4n
.i
−1
=
i
−i
4n
=
i
−(i
4
)
n
=
i
−(1)
n
…(i
4
=1)
=
i
−1
Now, multiplying numerator and denominator by i. We get,
=
i
2
−i
=
−1
−i
∴Z=i
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