# How do you simplify (2+i )/( 7+5i)?

Dec 1, 2015

$\frac{19}{74} - \frac{3}{74} i$

#### Explanation:

Multiply by the complex conjugate of the denominator.

$\frac{2 + i}{7 + 5 i} \cdot \frac{7 - 5 i}{7 - 5 i} = \frac{14 - 10 i + 7 i - 5 {i}^{2}}{49 - 35 i + 35 i - 25 {i}^{2}} = \frac{14 - 3 i - 5 {i}^{2}}{49 - 25 {i}^{2}}$

Recall that i=sqrt(-1, so ${i}^{2} = - 1$.

$\frac{14 - 3 i - 5 \left(- 1\right)}{49 - 25 \left(- 1\right)} = \frac{19 - 3 i}{74} = \frac{19}{74} - \frac{3}{74} i$

Note that the answer is written in the complex form $a + b i$.