Q9 of 202 Page 153

Prove that = 2i.

L.H.S.=

since = 1

= i

== -1

Now, applying the formula = 2ab

= .

= -1 + 1 + 2i

= 2i

L.H.S = R.H.S

Hence proved.

Prove that (1 + i¹⁰ + i²⁰ + i³⁰) is a real number.

Prove that = 2i.

= 2(1 – i).