Find the value of following expression:i30 + i80 + i120

i30 + i80 + i120 = i(28 + 2) + i80 + i120= (i4)7 × i2 + (i4)20 + (i4)30= – 1 + 1 + 1 = 1[since i4 = 1, i2 = – 1]i30 + i80 + i120 = 1

Q3 of 153 Page 13

Find the value of following expression:
i³⁰ + i⁸⁰ + i¹²⁰

i³⁰ + i⁸⁰ + i¹²⁰ = i^{(28 + 2)} + i⁸⁰ + i¹²⁰

= (i⁴)⁷ × i² + (i⁴)²⁰ + (i⁴)³⁰

= – 1 + 1 + 1 = 1

[since i⁴ = 1, i² = – 1]

i³⁰ + i⁸⁰ + i¹²⁰ = 1

Show that 1 + i¹⁰ + i²⁰ + i³⁰ is a real number ?

Find the value of following expression:

i⁴⁹ + i⁶⁸ + i⁸⁹ + i¹¹⁰

Find the value of following expression:

i + i² + i³ + i⁴

Find the value of following expression:

i⁵ + i¹⁰ + i¹⁵