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
`((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

`=((5+2i))/((6+i))\cdot((6-i))/((6-i))`

`=(30-5i+12i-2i^2)/(36-6i+6i-i^2)`

`=(30+7i-2i^2)/(36-i^2)`

`=(30+7i-2\left(-1\right))/(36-\left(-1\right))`

`=(30+7i+2)/(36+1)`

`=(32+7i)/(37)`

`=(32)/(37)+(7)/(37)i`

Hence final answer is
`(32)/(37)+(7)/(37)i`