Q12 of 202 Page 153

Prove tha= 0.

L.H.S =

Since we know that i = .

So,

= i + 3 i

=4i + 15i + 6i - 25i

= 0

L.H.S = R.H.S

Hence proved.

Prove that (1 – i)ⁿ= 2ⁿ for all values of n N

Prove tha= 0.

Prove that (1 + i² + i⁴ + i⁶ + i⁸ + …. + i²⁰) = 1.