Question

Write the quotient in the form a + bi

5/6+2i​

plz answer only if you got an answer

Answer 1

Given:

`(5)/(6+2i)`

To find:

The quotient in the form a + bi.

Solution:

We have,

`(5)/(6+2i)`

Multiply numerator and denominator by 6-2i.

`=(5* (6-2i))/((6+2i)* (6-2i))`

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

`=(30-10i)/(36+4i^2)`

`=(30-10i)/(36+4(-1))`
`[\because i^2=-1]`

On further simplification, we get

`=(30-10i)/(36-4)`

`=(30-10i)/(32)`

`=(30)/(32)-(10i)/(32)`

`=(15)/(16)+(-(5)/(16))i`

Therefore, the form a+bi is
`(15)/(16)+(-(5)/(16))i`, where,
`a=(15)/(16)` and
`b=(-(5)/(16))`.