Question

Simplify 5+2i/6+i

A. 32 7
- ---- + ---- i
37 37
B. 32 7
- ---- - ---- i
37 37

C 32 7
---- - ---- i
37 37

D 32 7
---- + ---- i
37 37

Answer 1

Given problem is $\frac{(5+2i)}{(6+i)}$

To simplify that we need to multiply and divide by conjugate of the denominator

conjugate of denominator 6+i will be 6-i as we just need to change sign of the imaginary part

Now multiply and divide by 6-i

$=\frac{(5+2i)}{(6+i)}\cdot\frac{(6-i)}{(6-i)}$

$=\frac{30-5i+12i-2i^2}{36-6i+6i-i^2}$

$=\frac{30+7i-2i^2}{36-i^2}$

$=\frac{30+7i-2\left(-1\right)}{36-\left(-1\right)}$

$=\frac{30+7i+2}{36+1}$

$=\frac{32+7i}{37}$

$=\frac{32}{37}+\frac{7}{37}i$

Hence final answer is $\frac{32}{37}+\frac{7}{37}i$