Find the sum (in+ in+1 + in+2 + in+3), where n N.

We have in+ in+1 + in+2 + in+3= in+ in.i + in.i2 + in.i3= in (1+ i +i2 + i3)= in (1 + i -1 –i )= in (0) = 0

Q6 of 202 Page 212

Find the sum (iⁿ+ iⁿ⁺¹ + iⁿ⁺² + iⁿ⁺³), where n N.

We have iⁿ+ iⁿ⁺¹ + iⁿ⁺² + iⁿ⁺³

= iⁿ+ iⁿ.i + iⁿ.i² + iⁿ.i³

= iⁿ (1+ i +i² + i³)

= iⁿ (1 + i -1 –i )

= iⁿ (0) = 0

Evaluate (i⁴ⁿ⁺¹ – i^4n–1)

Evaluate.

Find the sum (i + i² + i³ + i⁴ +…. up to 400 terms)., where n N.

Evaluate (1 + i¹⁰ + i²⁰ + i³⁰).