Question

If i=Square root of -1, what is the value of i^3?
A.-1
B.i
C.1
D.-i

Answer 1

First we are going to reesribir the inaginario number:
i = root (-1)
i = (- 1) ^ (1/2)
Then, we have to
By properties of exponents:
i ^ 3 = i ^ 2 * i
Substituting the value of i:
i ^ 3 = ((- 1) ^ (1/2)) ^ 2 * i
Applying properties of exponents:
i ^ 3 = ((- 1) ^ (1/2)) * ((- 1) ^ (1/2)) * i
i ^ 3 = ((- 1) ^ ((1/2) + (1/2)) * i
i ^ 3 = ((- 1) ^ ((2/2)) * i
i ^ 3 = ((- 1) ^ (1) * i
i ^ 3 = -1 * i
i ^ 3 = - i
Answer:
D.-i