Q15 of 202 Page 153

Prove that n N.

L.H.S =

since = 1

= i

= -1

= i – 1 – i + 1 + i - 1……+i-1

As, all terms will get cancel out consecutively except the first two terms. so that will get remained will be the answer.

= i - 1

L.H.S = R.H.S

Hence proved.

Prove that i⁵³ + i⁷² + i⁹³ + i¹⁰² = 2i.

Prove that n N.

Simplify each of the following and express it in the form a + ib :

2(3 + 4i) + i(5 – 6i)