rationalise the following complex quotient 3i^12-i^9/2i+1

Question

Rationalise the following complex quotient

Answer 1

rationalise the following complex quotient 3i^12-i^9/2i+1

Q = (3i^(12) - i^9) / (2i + 1)

Using i^2 = -1, then i^(12) = (-1)^6 = 1, and i^9 = i^8*i = (-1)^4*i = i

i^12 = 1, i^9 = i

Therefore, Q = (3 - i) / (2i + 1)

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

Q = [6i - 2i^2 - 3 + i] / [-4 - 1]

Q = (7i - 1) / (-5)

Q = 1/5 – 7i/5