How do you simplify $\frac{2 + i}{3 + i}$ $(2+i) / (3+i)$ ?

Question

1345 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-18T02:56:30

$\frac{7}{10} + \frac{1}{10} i$ $7/10+1/10i$

Multiply by the complex conjugate of the denominator.

$\frac{2 + i}{3 + i} (\frac{3 - i}{3 - i}) = \frac{6 + i - i^{2}}{9 - i^{2}}$ $(2+i)/(3+i)((3-i)/(3-i))=(6+i-i^2)/(9-i^2)$

Recall that since $i = \sqrt{- 1}, i^{2} = - 1$ $i=sqrt(-1),color(red)(i^2=-1$ .

$= \frac{6 + i - (- 1)}{9 - (- 1)} = \frac{7 + i}{10} = \frac{7}{10} + \frac{1}{10} i$ $=(6+i-(-1))/(9-(-1))=(7+i)/10=7/10+1/10i$

How do you simplify 2+i3+i (2+i) / (3+i)?