Question

Evaluate [(-i+1)/i]³​

Answer 1

Step-by-step explanation:

[(-i + 1)/i]^3

[(-i) + 1]^3 / i^3

formula :

(a+b)^3 = a^3 + b^3 + 3ab^2 + 3a^2 b

= [(-i)^3 + (1)^3 + 3(-i)^2(1) + 3(1)^2(-i)] / i^3

= [(-i)^3 + 1 + 3i^2 - 3i] / i^3

Now, we know ---- (i^3 = -i) and (i^2 = -1)

= [-(-i) + 1 - 3 - 3i] / (-i)

= (i - 2 - 3i) / -i

= (-2 - 2i) / -i

= -2(1+i) / -i

= 2(1+i) / i