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

L.H.S = (1 + i10 + i20 + i30)= (1 + + )since = 1= i= -1= 1 + = 1 + -1 +1 + -1= 0, which is a real no.Hence, (1 + i10 + i20 + i30) is a real number.

Q8 of 202 Page 153

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

L.H.S = (1 + i¹⁰ + i²⁰ + i³⁰)

= (1 + + )

since = 1

= i

= -1

= 1 +

= 1 + -1 +1 + -1

= 0, which is a real no.

Hence, (1 + i¹⁰ + i²⁰ + i³⁰) is a real number.

Prove that = 0.

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

Prove that = 2i.