Question

State the equivalent form of

Answer 1

\[\frac{2}{3+i}\]

Answer 2

\[a) \frac{3-i}{4}\]
\[b) \frac{3-i}{5}\]
\[c)\frac{4-i}{4}\]
\[d) \frac{4-i}{5}\]

Answer 3

I said the answer was a but I got it wrong. It says that it suppose to be b can anyone explain?

Answer 4

\[\frac{2}{3+i} = \frac{2}{3+i} \frac{3-i}{3-i} = \frac{2(3-i)}{3^2 -i^2} = \frac{2(3-i)}{9-(-1)} = \frac{3-i}{5}\]

Answer 5

because i is a radical... you cannot have a radical in the denominator so you need to rationalize the denominator so that the radical goes away from the denom..... so you multiply everything times its conjugate and simplify