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

Q14 of 202 Page 153

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

L.H.S = i⁵³ + i⁷² + i⁹³ + i¹⁰²

Since = 1

= i (where n is any positive integer )

= -1

= i + 1 + i +

= i+1+i-1

=2i

L.H.S = R.H.S

Hence proved.

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

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

Prove that n N.