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