Question

Prove that (-1√−1)⁴n+³= 1​

Answer 1

Answer:

Sqr_root(-1) = i

. I*i = i^2 = -1 by definition of square root

Similarly, i^3 = -i and i^4=1

Now i^5 =i and this continues with a period of 4.

Now. (- i) ^4n + 3 is equivalent to (-i)^3

=> The answer is -(i)^3 = -(-i) = i.