Question

express 1÷i +2÷i^2 +3÷i^3 + 5÷i^4 in the form a+ib​

Answer 1

Solution :

We know that, i = √(- 1)

Then, i² = - 1, i³ = - i and i⁴ = 1

∴ 1/i + 2/i² + 3/i³ + 5/i⁴

= 1/i + 2/(- 1) + 3/(- i) + 5/1

= 1/i - 2 - 3/i + 5

= (5 - 2) + (1/i - 3/i)

= 3 - 2/i

= 3 + 2i²/i [ ∵ i² = - 1 ]

= 3 + 2i ,

which is the required expression.

Answer 2

Answer:

l/i + 2/i² + 3/i³ + 5/i⁴

= 1/i -2 - 3/i + 5

= 1/i - 3/i + 3

= -2/i + 3

= (-2+3i) / i

= [ (-2+3i) × (0-i)] / [0² - i²]

= ( 2i - 3i²) / 1

= (2i + 3)