Question

7) Evaluate the following:
i) i35 ii) i888 iii) i93 iv) i116
v) i403 vi) 1/i58 vii) i-888
viii) i30 +i40 + i50 + i60​

Answer 1

Given :  i³⁵

i⁸⁸⁸

i⁹³

i¹¹⁶

i⁴⁰³

1/i⁵⁸

i⁻⁸⁸⁸

i³⁰ + i⁴⁰ + i⁵⁰ + i⁶⁰

To Find : Evaluate/ Simplify

Solution:

i = √- 1

i² = - 1

i³ = i².i = - i

i⁴ =  (i²)² = (-1)² = 1

i³⁵  = i³².i³  = (i⁴)⁸(-i) =  1⁸(-i)  = -i

i⁸⁸⁸ = (i⁴)²²² = 1²²² = 1

i⁹³ = i⁹².i =( i⁴)²³.i  =  1²³.i  = i

i¹¹⁶  = (i⁴)²⁹ = 1²⁹ = 1

i⁴⁰³ =  (i⁴)¹⁰⁰.i³  = -i

1/i⁵⁸   =  i²/i⁶⁰ =  - 1/(i⁴)¹⁵ = - 1

i⁻⁸⁸⁸  = (i⁴)⁻²²² = 1⁻²²² = 1/1²²² = 1/1  = 1

i³⁰ + i⁴⁰ + i⁵⁰ + i⁶⁰  = (i⁴)⁷.i² + (i⁴)¹⁰ + (i⁴)¹².i² + (i⁴)¹⁵

= - 1 + 1 - 1 + 1

= 0

Learn more:

find the value of i+i2+i3+i4​ - Brainly.in

https://brainly.in/question/12164128

Answer 2

Answer:

i2= (-1)

i3= -i

i4 =1

i18= -1