Question

Q.1
If n be a + ive integer, then show that
(1+1)
where i = V-1
(1- i) 1-2
= 2 in-1​

Answer 1

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